3) President Trump’s approval rating is 42%. Suppose that 10 people were chosen at random

a) Find the probability that 5 of the 10 people approve of the job President Trump is doing.

b) Find the probability that at most 3 of the 10 people approve of the job President Trump is doing.

c) Find the probability that at least 3 of 10 people approve of the job President Trump is doing.

A computer chip manufacturer finds that, historically, for ever 100 chips produced, 85 meet specifications, 10 need reworking, and 5 need to be discarded. Ten chips are chosen for inspection. A) What is the probability that all 10 meet specs? B) What is the probability that 2 or more need to be discarded? C) What is the probability that 8 meet specs,1 needs reworking, and 1 will be discarded?

Suppose that I ask you to lend me $200 for one year at a 5% promised interest rate. You believe that I will fully pay you the $210 with 95% probability; that I will only repay $100 with 1% probability; and that I will repay nothing with 4% probability. What promised interest rate should you have charged to ensure yourself an expected return of 5%?

8) Scores on an exam have a normal distribution with a mean of 80 and a standard deviation of 12.

a) Find the probability that a person would score above 90.

b) Find the probability that a person would score between 75 and 85.

c) Find the probability that a group of 7 people would have a mean score above 84.

d) Find the score needed to be in the top 10% of the class.

4. (5pts) At MCPHS university, there are three mathematics courses: Algebra (A), Calculus (C), and Statistics (S). Records show that 45% of students take A, 35% take C, 30% take S, 10% take both A and C, 8% take A and S, 5% take C and S, and 3% take A, C, and S.

a. Find the probability of those who only take A.

b. Find the probability of those who only take one mathematics course.

c. Find the probability of those who take at least one mathematics course.

d. Find the probability of those who did not take any mathematics course.

A box in a supply room contains 19 compact fluorescent lightbulbs, of which 7 are rated 13-watt, 8 are rated 18-watt, and 4 are rated 23-watt. Suppose that three of these bulbs are randomly selected. (Round your answers to three decimal places.)

(a) What is the probability that exactly two of the selected bulbs are rated 23-watt?


(b) What is the probability that all three of the bulbs have the same rating?


(c) What is the probability that one bulb of each type is selected?


(d) If bulbs are selected one by one until a 23-watt bulb is obtained, what is the probability that it is necessary to examine at least 6 bulbs?

A researcher investigating the accuracy of a certain pregnancy test finds the following

a) What is the probability that a randomly selected woman taking this pregnancy test is pregnant?

b) What is the probability that a randomly selected woman taking this pregnancy received a false positive (a false positive is testing positive and not being pregnant)?

c) Given a woman receives a positive pregnancy test, what is the probability that she is truly pregnant?

d) Are Test Result and True Status independent? Support your conclusion using probability formulas.

in middle earth, brave warriors come in all shapes and sizes. The following table lists the standardized height of combatants on the left and the frequency of their being present in the army on the right.

0 10

1 50

2 1000

3 300

4 50

a) find the relative frequency, probability (of each category), mean, and standard deviation

b) What is the probability a randomly selected combatant will be from Height class 3 or Height Class 4?

c) What is the probability that a randomly selected combatant will be in at least height class 2?

d) what is the probability that a randomly selected combatant will be at most in height class 3?

19. Which design is NOT appropriate for the one-sample t test?

a. Matched pairs

b. A design with one group

c. A design with two groups, each with different subjects

d. A design with two groups, each with the same subjects

20. What does a p-value tell you, in a test with H_a : μ > 0?

a. The probability of observing a score less than the observed score

b. The probability of observing a score equal to the observed score

c. The probability of observing a score greater than the observed score, assuming the null hypothesis is true

d. The probability of observing a score greater than the observed score, assuming the null hypothesis is false