# Assume that a procedure yields a

Question 1
Assume that a procedure yields a binomial distribution with a trial repeated n times. use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. n = 4, x = 3, p = 1/6.
0.015
0.004
0.012
0.023

Question 2
use Bayes' theorem to find the indicated probability.
5.8% of a population is infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease.
What is the probability that the person has the disease given that the test result is positive?
0.905
0.585
0.038
0.475

Question 3
If the random variable x has a Poisson Distribution with mean equal to 3, find the probability that x = 5. Round to 3 decimal places.
0.126
0.274
0.101
0.017

Question 4
Solve the problem.
Given the following sample data: 1.3, 2.2, 2.7, 3.1, 3.3, 3.7, use quantile() in R with type = 2 to find the estimated 63rd percentile. Pick the correct answer.
3.10
3.18
3.14
3.16

Question 5
Solve the problem.
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If a random sample of 40 mechanics is selected, find the probability that their mean rebuild time exceeds 8.7 hours. Assume the mean rebuild time has a normal distribution. (Hint, interpolate in the tables or use pnorm().)
0.129
0.135
0.195
0.146

Question 6
Find the mean for the binomial distribution with the number of trials n = 676 and the probability of success p = 0.7.
474.5
473.2
474.9
471.7

Question 7
The given values are discrete (binomial outcomes). Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability.
The probability of more than 44 correct answers.
The area to the left of 44.5
The area to the right of 44.5
The area to the right of 44
The area to the right of 43.5

Question 8
Solve the problem. Round to the nearest tenth unless indicated otherwise.
In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find P45 (45th percentile).
1148.1
1087.8
1022.6
1078.3

Question 9
Find the indicated probability.
In a homicide case 4 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 4 witnesses would pick the same person. (Hint-there is more than one way the witnesses can agree.)
0.008
0.001
0.8
0.0016

Question 10
Find the indicated probability.
An IRS auditor randomly selects 3 tax returns from 49 returns of which 7 contain errors. What is the probability that she selects none of those containing errors? Round to four decimal places.
0.6097
0.0019
0.0029
0.6231