If a person is vaccinated properly, the probability of hisher getti.pdf
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If a person is vaccinated properly, the probability of his/her getting a certain disease is .05. Without a vaccination, the probability of getting the disease is .35. Assume that 1/3 of the population is properly vaccinated. If a person gets the disease, what is th probability that he/she was vaccinated? Solution Probability = (1/3*.05)/(1/3*.05+2/3*.35) P = 0.0666.
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If a rock is thrown upward on the planet Mars with a velocity of 13 .pdf
If a rock is thrown upward on the planet Mars with a velocity of 13 m/s, its height in meters t
seconds later is given by y =( 13t - 1.86t^2)... (Round your answers to two decimal places.)
(a) Find the average velocity over the given time intervals.
(i) [1, 2]
______ m/s
(ii) [1, 1.5]
______ m/s
(iii) [1, 1.1]
______ m/s
(iv) [1, 1.01]
______ m/s
(v) [1, 1.001]
______ m/s
Solution
To find average velocity, you simply have to find the total distance divided by the total time for
each interval:
(i) Time = 2 - 1 = 1s
Distance = (13(2) - 1.86(2)2) - (13(1) - 1.86(1)2) = 7.42 m.
Average velocity = 7.42m / 1s = 7.42 m/s.
(ii) T = .5s
D = (13(1.5) - 1.86(1.5)2) - (13(1) - 1.86(1)2) = 4.175 m
V = 4.175m / .5s = 8.35 m/s.
(iii) T = .1s
D = (13(1.1) - 1.86(1.1)2) - (13(1) - 1.86(1)2) = .9094 m
V = .9094m / .1s = 9.094 m/s.
(iv) T = .01s
D = (13(1.01) - 1.86(1.01)2) - (13(1) - 1.86(1)2) = .092614 m
V = .092614m / .01s = 9.2614 m/s.
(v) T = .001s
D = (13(1.001) - 1.86(1.001)2) - (13(1) - 1.86(1)2) = .00927814 m
V = .00927814m / .001s = 9.27814 m/s..
If a population of rabbits is increasing by 14 rabbits every month ,.pdf
If a population of rabbits is increasing by 14 rabbits every month , is the population increasing
exponentially or linearly? Explain your answer
Solution
Linearly
1st month = 14 rabits
2nd month = 14 + 14 = 28 rabit
3rd month = 14 + 14 + 14 = 42 rabbits
and so on
So, the relation will be
no. of rabbits = 14 * m
m= no. of months
m= 1, 2, 3.....
If a population is normally distributed with X = 500 and X = 50, a.pdf
If a population is normally distributed with ?X = 500 and ?X = 50, and a sample of 4 is selected,
the proportion of sample means between 450 and 550 will __________ the proportion of
individual values between 450 and 550.
a. Be less than
b. Be greater than
c. Be the same as
d. Not be comparable to.
Solution
b. Be greater than.
If a manager is trying to obtain an international assignment, what m.pdf
If a manager is trying to obtain an international assignment, what main cultural information does
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For the international assignment, what training might be addressed and how extensive should
the training be?
Solution
Decision-making is a mental activity which is an integral part of planning and action taking in a
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planning, policy-making, climbing the career ladder. People all over the world engage in these
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If a hypothesis test leads to incorrectly rejecting the null hypothe.pdf
If a hypothesis test leads to incorrectly rejecting the null hypothesis, a type II statistical error has
been made ??
Solution
H0is true Truly not guilty H1is true Truly guilty Accept Null Hypothesis Acquittal Right
decision Wrong decision Type II Error Reject Null Hypothesis Conviction Wrong decision
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If a fair coin is tossed 11 times, what is the probability that thre.pdf
If a fair coin is tossed 11 times, what is the probability that three or fewer heads are obtained?
Solution
The probability that X heads are obtained is 11CX * (1/2)^11 by the binomial
formula. Therefore, the probability that three or fewer heads are obtained is equal to (11C3 +
11C2 + 11C1 + 11C0)*(1/2)^11 = 232/2048 = 29/256..
If a data set of ten observations is used in a multiple regression a.pdf
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estimate will be 1.0. the independent variables will be correlated. the regression
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Solution.
if a couple plans to have 5 children, what is the probability that t.pdf
if a couple plans to have 5 children, what is the probability that they will have at least one girl?
Solution
Probability to have a girl = probability to have a boy = 1/2
Atleast one girl implies they can have 1,2,3,4 or 5 girls
P = (1/2)^1 * (1/2)^4 + (1/2)^2 *(1/2)^3 + (1/2)^3 *(1/2)^2 + (1/2)^4 *(1/2)^1 +(1/2)^5 *(1/2)^0
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If a rock is thrown upward on the planet Mars with a velocity of 13 .pdf
If a rock is thrown upward on the planet Mars with a velocity of 13 m/s, its height in meters t
seconds later is given by y =( 13t - 1.86t^2)... (Round your answers to two decimal places.)
(a) Find the average velocity over the given time intervals.
(i) [1, 2]
______ m/s
(ii) [1, 1.5]
______ m/s
(iii) [1, 1.1]
______ m/s
(iv) [1, 1.01]
______ m/s
(v) [1, 1.001]
______ m/s
Solution
To find average velocity, you simply have to find the total distance divided by the total time for
each interval:
(i) Time = 2 - 1 = 1s
Distance = (13(2) - 1.86(2)2) - (13(1) - 1.86(1)2) = 7.42 m.
Average velocity = 7.42m / 1s = 7.42 m/s.
(ii) T = .5s
D = (13(1.5) - 1.86(1.5)2) - (13(1) - 1.86(1)2) = 4.175 m
V = 4.175m / .5s = 8.35 m/s.
(iii) T = .1s
D = (13(1.1) - 1.86(1.1)2) - (13(1) - 1.86(1)2) = .9094 m
V = .9094m / .1s = 9.094 m/s.
(iv) T = .01s
D = (13(1.01) - 1.86(1.01)2) - (13(1) - 1.86(1)2) = .092614 m
V = .092614m / .01s = 9.2614 m/s.
(v) T = .001s
D = (13(1.001) - 1.86(1.001)2) - (13(1) - 1.86(1)2) = .00927814 m
V = .00927814m / .001s = 9.27814 m/s..
If a population of rabbits is increasing by 14 rabbits every month ,.pdf
If a population of rabbits is increasing by 14 rabbits every month , is the population increasing
exponentially or linearly? Explain your answer
Solution
Linearly
1st month = 14 rabits
2nd month = 14 + 14 = 28 rabit
3rd month = 14 + 14 + 14 = 42 rabbits
and so on
So, the relation will be
no. of rabbits = 14 * m
m= no. of months
m= 1, 2, 3.....
If a population is normally distributed with X = 500 and X = 50, a.pdf
If a population is normally distributed with ?X = 500 and ?X = 50, and a sample of 4 is selected,
the proportion of sample means between 450 and 550 will __________ the proportion of
individual values between 450 and 550.
a. Be less than
b. Be greater than
c. Be the same as
d. Not be comparable to.
Solution
b. Be greater than.
If a manager is trying to obtain an international assignment, what m.pdf
If a manager is trying to obtain an international assignment, what main cultural information does
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if a couple plans to have 5 children, what is the probability that t.pdf
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Solution
Probability to have a girl = probability to have a boy = 1/2
Atleast one girl implies they can have 1,2,3,4 or 5 girls
P = (1/2)^1 * (1/2)^4 + (1/2)^2 *(1/2)^3 + (1/2)^3 *(1/2)^2 + (1/2)^4 *(1/2)^1 +(1/2)^5 *(1/2)^0
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-$50 billion; rose.
impossible to tell; impossible to tell.
-$100 billion; rose.
-$50 billion; fell.
-$50 billion; rose.
impossible to tell; impossible to tell.
-$100 billion; rose.
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If a coin is tossed five times, find the probability that
(a) The first toss matches the second toss.
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35
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Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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