1) A persons level of blood glucose and diabetes are closely relat.pdf

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1) A person\'s level of blood glucose and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12- hour fast, the random variable x will have a distribution that is approximately normal with mean mc033-1.jpg = 90 and standard deviation of mc033-2.jpg = 29. What is the probability that, for an adult after a 12-hour fast, x is between 85 and 137? Answer a. 0.432 b. 0.500 c. 0.516 d. 0.053 e. 0.690 2) Find z such that 48.8% of the standard normal curve lies between -z and z. Answer a. 0.656 b. 0.936 c. 0.205 d. 0.154 e. 0.123 3) The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height mc050-1.jpg of a sample of ten 18-year-old men will be between 69 and 71 inches? Answer a. 0.1461 b. 0.8539 c. 0.2922 d. 0.1611 e. 0.3539 4) The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the average height mc049-1.jpg of a sample of ten 18-year-old men will be less than 70 inches? Round your answer to four decimal places. Answer a. 0.0174 b. 0.4826 c. 0.4913 d. 0.9826 e. 0.9652 5) How do frequency tables, relative frequencies, and histograms showing relative frequencies help us understand sampling distributions? Answer a. They help us visualize the probability distribution through tables and graphs that approximately represent the random sampling distribution. b. They help us to measure or estimate of the likelihood of a certain statistic falling within the class bounds. c. They help us visualize the sampling distribution through tables and graphs that approximately represent the sampling distribution. d. They help us visualize the probability distribution through tables and graphs that approximately represent the population distribution. 6) True or False? The standard error of a sampling distribution is the difference between the mean and the standard deviation. Answer True False 7) The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that an 18-year-old man selected at random is greater than 72 inches tall? Answer a. 0.0918 b. 0.1836 c. 0.8164 d. 0.9082 e. 0.4082 8) What is the standard deviation of a sampling distribution called? Answer a. the variance b. the mean c. the expected value d. the standard error 9) Assuming that the heights of college women are normally distributed with mean 63 inches and standard deviation 3.5 inches, what percentage of women are taller than 56 inches? Answer a. 97.7% b. 99.9% c. 84.1% d. 2.3% e. 50.0% 10) Is the standard score positive or negative when the raw score is 6 and the mean is 4? Answer a. The standard score is negative. b. The standard score is positive. 11) Find the area under the standard normal curve over the i.

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and standard deviation 3 inches. What is the probability that the average height mc049-1.jpg of
a sample of ten 18-year-old men will be less than 70 inches? Round your answer to four decimal
places.
Answer
a. 0.0174
b. 0.4826
c. 0.4913
d. 0.9826
e. 0.9652
5) How do frequency tables, relative frequencies, and histograms showing relative frequencies
help us understand sampling distributions?
Answer
a. They help us visualize the probability distribution through tables and graphs that
approximately represent the random sampling distribution.
b. They help us to measure or estimate of the likelihood of a certain statistic falling within the
class bounds.
c. They help us visualize the sampling distribution through tables and graphs that approximately
represent the sampling distribution.
d. They help us visualize the probability distribution through tables and graphs that
approximately represent the population distribution.
6) True or False? The standard error of a sampling distribution is the difference between the
mean and the standard deviation.
Answer
True
False
7) The heights of 18-year-old men are approximately normally distributed with mean 68 inches

and standard deviation 3 inches. What is the probability that an 18-year-old man selected at
random is greater than 72 inches tall?
Answer
a. 0.0918
b. 0.1836
c. 0.8164
d. 0.9082
e. 0.4082
8) What is the standard deviation of a sampling distribution called?
Answer
a. the variance
b. the mean
c. the expected value
d. the standard error
9) Assuming that the heights of college women are normally distributed with mean 63 inches
and standard deviation 3.5 inches, what percentage of women are taller than 56 inches?
Answer
a. 97.7%
b. 99.9%
c. 84.1%
d. 2.3%
e. 50.0%
10) Is the standard score positive or negative when the raw score is 6 and the mean is 4?
Answer
a. The standard score is negative.
b. The standard score is positive.
11) Find the area under the standard normal curve over the interval specified below.To the left
of z = 0

Answer
a. 0.841
b. 0.001
c. 0.023
d. 0.159
e. 0.500
12) Assuming that the heights of college women are normally distributed with mean 62 inches
and standard deviation 3.5 inches, what percentage of women are between 58.5 inches and 72.5
inches?
Answer
a. 34.1%
b. 84.0%
c. 15.7%
d. 13.6%
e. 97.6%
13) Raul received a score of 61 on a history test for which the class mean was 51 with standard
deviation 5. He received a score of 71 on a biology test for which the class mean was 66 with
standard deviation 5. On which test did he do better relative to the rest of the class?
Answer
a. history
b. biology
Solution
(3) P(69

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Page 1 of 10 Class Time_______________ Day_____________________ School of Business Business Statistics I Exam 5 Print out this test. Do all your calculations on the test and mark your final answer on the scantron sheet (answer sheet. If you don’t have a scantron sheet, one will be provided in the class.Turn‐in both your test and the answer sheet. Do not forget to write your name, Id#, and class time on both the answer sheet and the test. Name____________________________________ID #______________ 1. Suppose a random sample of 36 items is selected from a population. The population standard deviation is known to be 10. The standard error of the mean would be: (a) 1.333 (b) 1.667 (c) 3.667 (d) 2.333 (e) 1.875 2. From 100 homes of similar sizes, a sample of 25 homes is selected to study the average home heating cost during the winter months. Suppose the heating cost is known to be normally distributed with mean of $220 per month for the four months of winter and standard deviation of $45. If the 100 homes represent the population size, the standard error of the heating cost would be: (a) 9.00 (b) 8.75 (c) 3.66 (d) 7.83 (e) 1.87 3. Suppose n=64 measurements is selected from a population with mean 20  and standard deviation 16  . The Z‐score corresponding to a value of 24x  would be: (a) 2.0 (b) 3.0 (c) ‐2.5 (d) ‐2.0 Page 2 of 10 (e) 1.5 4. A random sample of n=100 observations is selected from a population with 30  and standard deviation 16  . The probability that ( 28)p x  is (a) 0.8236 (b) 0.8936 (c) 0.9036 (d) 0.9983 (e) 0.8944 5. A random sample of n=100 observations is selected from a population with 30  and standard deviation 16  . The probability that (22.1 26.8)p x  is (a) 0.0434 (b) 0.0228 (c) 0.0036 (d) 0.0983 (e) 0.0944 6. A random sample of size 36 is drawn from a population with mean 278  . If 86% of the time the sample mean is less than 281, then the population standard deviation would be: (a) 16.67 (b) 12.67 (c) 11.12 (d) 13.33 (e) 19.67 7. A random sample of size n=81 is drawn from population with mean equal to 50 and standard deviation 25. The expected value of the mean ( )iE x [or, x ] and the standard error x  (a) 50 and 2.95 (b) 50 and 2.78 (c) 28 and 1.72 (d) 50 and 15.00 (e) 80 and 12.0 8. According to a recent news report, the average price of gasoline is $3.80 per gallon (March 2011). This price can be considered as the nationwide population mean price per gallon. Suppose that the standard deviation of the gasoline price per gallon is $0.50. A sample of 49 gas stations in Salt Lake City is taken. The probabilit.

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8. Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph. a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit? b. What proportion of the vehicles would be going less than 50 mph? c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion? d. In what way do you think the actual distribution of speeds differs from a normal distribution? Ans. a. m = 71 mph; s = 8 mph The proportion of vehicles less than or equal to the speed limit 65 mph = 0.2266 b. The proportion of the vehicles would be going less than 50 mph = 0.0043 c. The new speed limit would be 81.25 mph (approximately 81 mph). d. The actual distribution of speeds on a highway differs from the normal distribution in that i. It is not symmetric. The speeds are not symmetrically distributed about the central vaue. Two speeds that are an equal amount greater or lower than the mean speed, may not have the same frequency as is required for a normal distribution. ii. Secondly, the speeds further away from the average speed do not drop in frequency as rapidly as in normal distribution. The frequency of the extreme values may not be as low as in normal distribution, resulting in a fatter tail. The distribution may also be skewed in one direction. This is especially true in highways where the distribution will be expected to be positively skewed- greater frequency in the higher speed range than lower. 11. A group of students at a school takes a history test. The distribution is normal with a mean of 25, and a standard deviation of 4. (a) Everyone who scores in the top 30% of the distribution gets a certificate. What is the lowest score someone can get and still earn a certificate? (b) The top 5% of the scores get to compete in a statewide history contest. What is the lowest score someone can get and still go onto compete with the rest of the state? Ans . For the test, the mean score m = 25; s = 4 Using the normal calculator (Ch-7, Lane), a. the lowest score someone can get and still earn a certificate = 27.096 (or approx.. 27.1) b. the lowest score someone can get and still go onto compete with the rest of the state = 31.58 (or approx. 31.6) 12. Use the normal distribution to approximate the binomial distribution and find the probability of getting 15 to 18 heads out of 25 flips. Compare this to what you get when you calculate the probability using the binomial distribution. Write your answers out to four decimal places. Ans For the binomial distribution of coin flipping, probability of getting a head (success) in one flip = p = 0.5 N = no. of trials = 25 Mean is m = N*p = 25 * 0.5 = 12.5 Variance σ 2 = Np(1-p) = (25)(0.5)(0.5) = 6.25 The standard deviation is therefore σ .

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1. Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second normal distribution has a mean of 10 and a standard deviation of 2. Which of the following is true? A) The locations of the distributions are different. B) The distributions are from two different families of distributions. C) The dispersions of the distributions are different. D) The dispersions of the distributions are the same. 2. When testing for differences between treatment means, a confidence interval is computed with __________________. A) The mean square error B) The standard deviation C) The sum of squared errors D) The standard error of the mean 3. Which symbol represents a test statistic used to test a hypothesis about a population mean? A) α B) β C) μ D) z 4. If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate? A) -1 B) +1 C) 0 D) Infinity 5. Twenty randomly selected statistics students were given 15 multiple-choice questions and 15 open-ended questions, all on the same material. The professor was interested in determining if students scored higher on the multiple-choice questions. This experiment is an example of ________________. A) A one-sample test of means B) A two-sample test of means C) A paired t-test D) A test of proportions 6. An ANOVA has three sources of variation. They are _____, _____, and _____. 7. The Intelligence Quotient (IQ) test scores for adults are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability we could select a sample of 50 adults and find the mean of this sample is less than 95? A) 0.0091 B) 0.9818 C) 0.4909 D) 0.9544 8. What distribution does the F distribution approach as the sample size increases? A) Binomial B) Normal C) Poisson D) Exponential 9. A national manufacturer of unattached garages discovered that the distribution of the time for two construction workers to erect the Red Barn model is normally distributed with a mean of 32 hours and a standard deviation of 2 hours. What percent of the garages take between 32 and 34 hours to erect? A) 16.29% B) 76.71% C) 3.14% D) 34.13% 10. The F distribution is a ______________ distribution. 11. The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the population mean. He selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95% confidence interval for the population mean? A) 14.7 and 16.9 B) 13.2 and 17.6 C) 10.0 and 20.0 D) 16.1 and 18.1 12. A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their average age was 19.1 years with a sample standard deviation of 1.5 years. What is the best point estimate for the population mean? A) 2.1 years B) 1.5 years C) 19.1 years D) 9 years 13. The statistical.

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