BUS216 Exam #3 Review – SP14 1 1. In order to have the standard error of the mean be 12, one would need to take _______ samples from a normally distributed population with a standard deviation of 48. 2. The average price of cell phones manufactured by Ahmadi, Inc. is $98 with a standard deviation of $12. Furthermore, it is known that the prices of the cell phones manufactured by Ahmadi are normally distributed. a. What percentage of cell phones produced by Ahmadi, Inc. will have prices of at least $120.20? b. Cell phones with prices of at least 81.80 will get a free gift. What percentage of the cell phones will be eligible for the free gift? c. What are the minimum and the maximum values of the middle 95% of cell phone prices? d. If 7,218 of the Ahmadi cell phones were priced at least $119.00, how many cell phones were produced by Ahmadi, Inc.? 3. A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation. 4. Catherine Chao, Director of Marketing Research, needs a sample of Kansas City households to participate in the testing of a new toothpaste package. 40% of the households in Kansas City prefer the new package. Catherine conducts a random sample of 300 households in Kansas City asking them whether or not they prefer the new packing. What is probability that in Catherine's random sample of 300 households more than 135 prefer the new package 5. MNM Corporation gives each of its employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 25 is taken from a population. (a) What is the probability that the average aptitude test in the sample will be between 70.14 and 82.14? (b) What is the probability that the average aptitude test in the sample will be greater than 82.68? 6. A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 10. a) The professor has informed us that 16.6 percent of her students received grades of A. What is the minimum score needed to receive a grade of A? BUS216 Exam #3 Review – SP14 2 b) If 12.1 percent of her students failed the course and received F's, what was the maximum score among those who received an F? c) If 33 percent of the students received grades of B or better (i.e., A's and B's), what is the minimum score of those who received a B? 7. .A large disaster cleaning company estimates that 30% of the jobs it bids on are finished within the bid time. Looking at a random sample of 8 jobs that is has contracted; find the probability that x (number of jobs finished on time) is within one standard deviation of the mean. 0.6826 ...

1. BUS216 Exam #3 Review – SP14
1
1. In order to have the standard error of the mean be 12, one
would need to take
_______ samples from a normally distributed population with a
standard
deviation of 48.
2. The average price of cell phones manufactured by Ahmadi,
Inc. is $98 with a
standard deviation of $12. Furthermore, it is known that the
prices of the cell
phones manufactured by Ahmadi are normally distributed.
a. What percentage of cell phones produced by Ahmadi, Inc.
will have prices of at
least $120.20?
b. Cell phones with prices of at least 81.80 will get a free gift.
What percentage of
the cell phones will be eligible for the free gift?
c. What are the minimum and the maximum values of the middle
95% of cell
phone prices?

2. d. If 7,218 of the Ahmadi cell phones were priced at least
$119.00, how many cell
phones were produced by Ahmadi, Inc.?
3. A manufacturing process produces items whose weights are
normally
distributed. It is known that 22.57% of all the items produced
weigh between
100 grams up to the mean and 49.18% weigh from the mean up
to 190 grams.
Determine the mean and the standard deviation.
4. Catherine Chao, Director of Marketing Research, needs a
sample of Kansas City
households to participate in the testing of a new toothpaste
package. 40% of the
households in Kansas City prefer the new package. Catherine
conducts a random
sample of 300 households in Kansas City asking them whether
or not they prefer
the new packing. What is probability that in Catherine's random
sample of 300
households more than 135 prefer the new package
5. MNM Corporation gives each of its employees an aptitude
test. The scores on the
test are normally distributed with a mean of 75 and a standard
deviation of 15. A
simple random sample of 25 is taken from a population.

3. (a) What is the probability that the average aptitude test in the
sample will be
between 70.14 and 82.14?
(b) What is the probability that the average aptitude test in the
sample will be
greater than 82.68?
6. A professor at a local university noted that the grades of her
students were
normally distributed with a mean of 78 and a standard deviation
of 10.
a) The professor has informed us that 16.6 percent of her
students received
grades of A. What is the minimum score needed to receive a
grade of A?
BUS216 Exam #3 Review – SP14
2
b) If 12.1 percent of her students failed the course and received
F's, what was
the maximum score among those who received an F?

4. c) If 33 percent of the students received grades of B or better
(i.e., A's and B's),
what is the minimum score of those who received a B?
7. .A large disaster cleaning company estimates that 30% of the
jobs it bids on are
finished within the bid time. Looking at a random sample of 8
jobs that is has
contracted; find the probability that x (number of jobs finished
on time) is within
one standard deviation of the mean. 0.6826
8. The length of time patients must wait to see a doctor in a
local clinic is uniformly
distributed between 15 minutes and 2 1/2 hours.
a. What is the probability that a patient would have to wait
between ¾ of an
hour and 2 hours?
b. Calculate the probability that a patient would have to wait
over 2 hours. .222
9. X is a normally distributed random variable with a mean of 8
and a standard
deviation of 4.0. Find the value of X for which 70.54% of the
area under the
distribution curve lies to the right of it. (Note: the diagram is
not necessarily to
scale.)

5. BUS216 Exam #3 Review – SP14
3
10. The average age of vehicles registered in the United States
is 96 months.
Assume the population is normally distributed with a standard
deviation of
15 months. Find the probability that the mean age of a sample
of 36 vehicles
is between 98 and 100 months?
11. A survey of 250 lobster fishermen found that they catch an
average of 32.0
pounds of lobster per day with a standard deviation of 4.0
pounds. If a random
sample of 36 lobster fishermen is selected, what is the
probability that their
average catch is less than 31.5 pounds? Assume the distribution
of the weights of
lobster is normal.
12. DRUGS R US" is a large manufacturer of various kinds of
liquid vitamins. The
quality control department has noted that the bottles of

6. vitamins marked 6
ounces vary in content with a standard deviation of 0.3 ounces.
Assume the
contents of the bottles are normally distributed.
a) What percentage of all bottles produced contains more than
6.51 ounces of vitamins?
b) What percentage of all bottles produced contains less than
5.415 ounces?
c) What percentage of bottles produced contains between 5.46
to
6.495 ounces
d) Ninety-five percent of the bottles will contain at least how
many ounces?
e) What percentage of the bottles contains between 6.3 and 6.6
ounces? 13.59%
To kick off our San Francisco series of engineer-to-engineer
lectures on new technologies and interesting problems in
consumer software, we invited in the Great Alex Payne to talk
about how Twitter uses Scala, a programming language that
combines traits of object-oriented languages and functional
languages with an eye toward supporting concurrency better in
large-scale software.
Alex started at Twitter in 2007, working remotely in
Washington DC, when there were “only one and a half
engineers.” Now, Twitter has 170 engineers. “It has been an
interesting process,” Alex said. Right after his talk, Alex
packed up his cats and headed for Portland, where he’ll still

7. work for Twitter, but ensconced in a smaller, more closely-knit
community. Here are his thoughts on Scala (Alex talks fast, and
doesn’t waste many word, so my hands were in a rictus of agony
from trying to type what he wrote) :
Best, Glenn at Redfin
I started working the programming interface when we were at
this very early stage. Now, it handles a couple billion
operations every day. It is being baked into more and more of
the Web.
I’ve spent the past year working on Twitter’s infrastructure. For
that, we use a weird language called Scala. I worked on a book
for O’Reilly about Scala that you could sit down with over a
three-day weekend to get up to speed on the language.
Why Use Scala?
Why use Scala when you have Ruby and Ruby on Rails? Well,
we still use Rails. It works great for front-end stuff. The
productivity is worth the tradeoff for working in a slower-
performing dynamic language. When you think about what a
web framework is doing under the hood, it’s tons and tons of
string concatenation. Ruby on Rails can handle that.
What we had a need for as Twitter grew was for long-running
heavy processes, message-queuing, caching layers for doing
20,000 operations a second. Ruby garbage-collection is tough,
Ruby doesn’t do really well with long-running processes.
Languages Twitter Considered
We knew we needed another language. How did we pick a
language that was really fun for us? We considered Java, C/C++
of course. And we looked at Haskell and OCaml for functional
programming, though neither has gotten much commercial use.
Erlang developers are doing stuff with a lot of network I/O but
not with a lot of disk I/O; the knowledge-base around the
language wasn’t great though, and the community seemed
inaccessible.
Java is easy to use, but it’s not very fun, especially if you’ve
been using Ruby for a while. Java’s productive, but it’s just not
sexy anymore. C++ was barely considered as an option. Some

8. guys said, if I have to work in C++ again, I’m going to stab my
eyes out with a shrimp fork. Java-script on the server-side via
Rhino had performance problems, and it wasn’t quite there yet
when we were evaluating it.
So what were our criteria for choosing Scala? Well first we
asked, was it fast, and fun, and good for long-running process?
Does it have advanced features? Can you be productive quickly?
Developers of the language itself had to be accessible to us as
we’d been burned by Ruby in that respect. Ruby’s developers
had been clear about focusing it on fun, even sometimes at the
expense of performance. They understood our concerns about
enterprise-class support and sometimes had other priorities.
We wanted to be able to talk to the guys building the language,
not to steer the language, but at least to have a conversation
with them.
Was Scala Fast?
And did Scala turn out to be fast? Well, what’s your definition
of fast? About as fast as Java. It doesn’t have to be as fast as C
or Assembly. Python is not significantly faster than Ruby. We
wanted to do more with fewer machines, taking better advantage
of concurrency; we wanted it to be compiled so it’s not burning
CPU doing the wrong stuff.
What Alex Likes About Scala
Scala is a lot of fun to work in; yes, you can write staid, Java-
like code when you start. Later, you can write Scala code that
almost looks like Haskell. It can be very idiomatic, very
functional — there’s a lot of flexibility there.
And it’s fast. The principal language developer at Scala worked
on the JVM at Sun. When Java started, it was clearly a great
language, but the VM was slow. The JVM has been brought to
the modern age and we don’t think twice about using it.
Scala can borrow libraries from Java libraries; you’re compiling
down to Java byte code, and it’s all calling back and forth in a
way that is really efficient. We haven’t run into any library
dependencies that cause problems. We can hire people with Java
and they can do pretty well.

9. The community is small but growing, and it’s really accessible.
We got to sit down with Martin and ask him and his team about
funding for Scala, how problems with Scala will get solved.
We’ve never really had to call on that level of access, but it’s
really nice to know it’s there.
The Grand Unified Theory of Scala
The grand unified theory of Scala is that it combines objective-
oriented programming (OOP) and functional programming (FP).
Scala’s goal is to essentially say OOP and FP don’t have to be
these separate worlds. It’s kind of zen, and you don’t get it
when you first start. It’s really, really powerful; it’s nice to
have a language with a thesis, rather than trying to appeal to
every programmer out there. Scala is trying to solve a specific
intellectual problem.
You have methods that take anything between a string and
several point away on the inheritance chain from a string. The
syntax is more flexible than Java; it’s very human-readable, as
you can leave out period between method calls so it looks like a
series of words. Your program can make nice declarative
statements about the logic of what you’re trying to do.
Traits, Pattern-Matching, Mutability
With Scala, you can also use traits. This is handy because of
course you have cross-cutting concerns in your application. For
example, every object needs to be able to log stuff, but you
don’t want everything extending from a logger class — that’s
crazy. With Scala, you can use a trait to shove that right in, and
you can add as many traits as you like to a given class or object.
You can choose between mutability and immutability. This can
be dangerous. 9 out of 10 times you use immutable variables
when you want predictability, especially when you have stuff
running concurrently. But Scala trusts the programmer for
mutability when he or she needs it.
Scala has the concept of lazy values – you can say lazy val x = a
really complicated function. That isn’t going to be calculated
until the last second, when you need that value. This is nice.
Pattern-matching is nice too. It lets you dive into a data

10. structure so you can, for example, explode out a collection that
matches an array with “2” as its third element. You can break
out strings and regular expressions, and you can pattern-match
groups with regular expressions.
An oddball feature that is really useful is the ability to use XML
literals, so that you can make something equal to an XML
literal, as if the XML literal is a string. You don’t have to
import Sax or some crazy XML library.
The Concurrency Story
When people read about Scala, it’s almost always in the context
of concurrency. Concurrency can be solved by a good
programmer in many languages, but it’s a tough problem to
solve. Scala has an Actor library that is commonly used to solve
concurrency problems, and it makes that problem a lot easier to
solve.
An Actor is an object that has a mailbox; it queues messages
and deals with them in a loop, and it can leave a message on the
floor when it doesn’t know what to do with it.
You can model concurrency as messages – a unit of work —
sent to actors, which is really nice. It’s like using a queuing
system. You can also use Java.util.concurrency stuff too, Netty
and Apache Mina, dropping it right in. You can rewrite the
Actor implementation, and some folks have gone so far as
rolling their own software transactional memory libraries.
Java interoperability is a big, big win. There are ten years of
great libraries, things like Jodatime. We use a lot of Hadoop and
it has been easy to wire Scala to the Hadoop libraries. We use
Thrift, without having to patch it; we use libraries from the
Apache Commons and from Google.
How Twitter Uses Scala
So that’s why we use Scala, but how do we use it?
In the enterprise world, a service-oriented architecture is not
new, but in Web 2.0 it is crazy new science. With PHP or Ruby
on Rails, when you need more functionality, you just include
more plugins and libraries, shoving them all in to the server.
The result is a giant ball of mud.

11. So anything that has to do heavy lifting in our stack is going to
be an independent service. We can load-test it independently,
it’s a nice way to decompose our architecture.
What services at Twitter are Scala-powered? We have a queuing
system called Kestrel. It uses a souped-up version of the mem-
cache protocol. We originally wrote it in Ruby — it got us
through a few weeks, but because Ruby is a dynamic language,
the service began to show its performance weak spots.
Flock to Store the Social Graph
We use Flock to store our social graph, as a denormalized list of
user ids. It’s not a graph database, so you can’t perform random
walks along the graph. But it’s great for quickly storing
denormalized sets of user ids, and doing intersections. We’re
doing 20,000 operations a second right now, backed by a
MySQL schema designed to keep as much as possible in
memory. It has been very efficient — not many servers are
needed.
Hawkwind for People Search
Our people-search is powered by a Scala-built service we called
Hawkwind. It’s a bunch of user objects dumped out by Hadoop,
where the request is fanned out to multiple machine and then
pulled back together.
Hosebird for Streaming
We stream out tweets to public search engines, using a low-
latency, HTTP-based, persistent connection system called
Hosebird. We looked at queuing systems that financial-services
companies use, but couldn’t find anything that could handle the
volume of the load. We built something on top of Jetty using
Scala. We have more Scala-powered services in the works that I
can’t talk about.
Thrift for Transferring Data
We use also Thrift, built at Facebook then open-sourced at
Apache. With Thrift, you can define data structures and
methods, and it deals with everything you don’t want to deal
with to efficiently represent data and get it from point A to
point B. As your system evolves, your method signatures

12. change, and Thrift has a nice system for creating positional
arguments and being backwards compatible.
These services make our life a lot easier. We often staff projects
with two people who are pair programming, sitting together for
six or eight weeks. These guys can build something like people-
search in a couple of months.
The only problem with so many different teams is that there is
some divergence in terms of operational approaches – we have
to work with ops guys to monitor the right stuff, be it disk or
memory or what have you — but we can resolve that jitter over
time. We’re ok with the tradeoffs.
The Development Environment
OK, now let’s talk about the tools… the IDEs for Scala are not
up to snuff, that is true. IntelliJ IDEA is good but it’s
shockingly buggy. The solution we’ve settled on is just using a
plain text editor. We use EMACS, as there’s a really nice mode
for the build tool. That takes compile/test BS out of your
workflow. Of course, you can give the IDEs a try. Even though
I’m an IDE cynic, maybe they’ve improved; that said, a plain
text editor can be really productive.
Simple Build Tool
sbt is our Simple Build Tool, but it’s not simple or limited in
any way. It’s Scala’s answer to Ant and Maven, and really it’s a
superset of Ant and Maven. It’ll set up a new project, create a
nice project structure for you and manage dependencies — you
can slap ‘em right in by copying XML.
You can write your own build-tasks. We added support for
Thrift in an afternoon; it’s got a library for shelling out, as Java
is not so great at shell operations because it targets so many
platforms. sbt is well well documented. And the absolutely
coolest feature is that it’s got an interactive console interface
where you can type in code and see how it works.
So that means sbt can insert you in an interactive way into your
running program. This is great for debugging, great for
sketching code out. You have a nice workflow where you don’t
have to worry about compilation.

13. specs
We’re very test-driven, we’re not wedded to behavior-driven
development (BDD), but the best library in Scala is BDD-
oriented. You can throw in different mocking libraries, and it
works just as well in Scala as Java.
Libraries
We’ve built a bunch of libraries. We gather a lot of stats, I
mean, A LOT. We spent the first year of Twitter pushing
forward on features, but never thinking about what we were
building scientifically. That bit us in the ass in a big way.
You’ve probably seen a gradual increase in stability. At
conferences, people ask us if it was the switch from Ruby to
Scala, or if it was more machines. But really what did it was
gathering numbers on everything, setting metrics and trying to
improve.
Ostrich helps here. It is an in-process statistics gatherer, with
counters, gauges, timers. You can share stats via JMX, JSON-
over-HTTP etc. Hopefully it’s pretty simple to use and easy to
integrate.
Configgy manages configuration files and logging in a really
nice, flexible way. You can include config files in one another
and you can do inheritance; it throws in a really nice logging
wrapper, with lazy evaluation on the values you’re trying to log
so you don’t burn machine-time generating log statements. It
has a subscription API for pushing out a new config file. It’s a
little crazy to have our own config file format, but Scala makes
it work.
xrayspecs: this is an extension to specs, because we need a way
to test concurrent operations. Some of the extensions in
xrayspecs have been merged back into specs. We can freeze and
unfreeze time.
scala-json: this is a better Scala JSON codec. We’ve used this
really heavily in production for a while. If you need something
like this, hopefully it’ll do the job.
Other Twitter Scala libraries: Naggatti (protocol builder for
Apache Mina), Smile (Actor-powered memcached client),

14. Querulous (a nice SQL database client) and Jackhammer (a load
testing framework in its early stages). Check out GitHub for
more.
How Do we Teach People?
I think we’re employing at Twitter about half the people in the
world who know the Scala language. The other half are
academics or at Foursquare. Even though Scala’s getting more
and more popular, fundamentally we can’t hire people with
experience in the language.
Pair Programming, Code Reviews
To start people out, we pair program. It isn’t mandatory at
Twitter, but it’s a great way to learn Scala. We’ve come up with
a bunch of style guides. The good and bad thing is that Scala’s
going to be C++ in ten years, because there’s just a lot of
surface area and it can get complicated. For that reason, we are
pretty rigorous about a style code.
We do code reviews; it doesn’t go into the master branch if it
hasn’t been reviewed by your peers. Right now, I’m working
with a guy we hired from Google. He’s an amazing engineer, far
better than I am, but at first he didn’t know Scala.
When I looked at his code, there was absolutely nothing wrong
under the hood. But we’d go through and say, “Here’s where
this line could be a little more idiomatic from a Scala
perspective.” I do classes over lunch – but you need a big group
to commit to come every week. Then there’s my book, and
there’s other books: Dave Pollak’s book, the Odersky
book(Programming in Scala, aka “the stairway book”). If you
learn by example and need a desk reference, grab “the stairway
book.” Or search Google for a talk by my co-worker on “The
Seductions of Scala” for lots of examples
What Version of Scala Does Twitter Use?
We use 2.7. It’s got a couple of warts, particularly in the
collections classes. Scala 2.8 fixes a lot of those warts, and
there’s a bunch of performance work in there too, plus the
ability to have named arguments in your functions.
I’m co-organizing a Scala summit at the OSCON conference in

15. Portlandthis summer; come to that if you want to learn more!
There’s a great blog called DailyScala, where an engineer
writes about what he’s learning. I learn stuff from that guy all
the time…
And that was it! Many thanks to Alex for his magnificent talk,
and to all the lovely folks who visited our offices! We had a lot
of fun, we learned a ton, and now we’re looking forward on
May 20 to hearing from Cloudera’s Jay Hammerbacher — the
man who conceived of and built the data team at Facebook —
on Hadoop. Everyone’s invited!