Study Guide for final Exam

Question

(10) According to government data, the probability that an adult was never in a museum is 15%. A random sample of 25 adults were surveyed.



1. What is the probability that exactly three adults were never in a museum?
2. Find the mean and standard deviation of the number of adults that were never in a museum.

Answer 1

Jon S. has some good answers. But if you're doing the problems on the final exam, the first answer he's given might not be useful for you.

If you're using the TI 84 calculator, there's a function that gives you binomial probabilities. 2nd-> DISTR (the VARS key) brings up a list of functions for doing probability and statistics. If you scroll down to binompdf (this stands for binomial probability distribution function), you can enter the following:

trials: (the number of attempts at success) : 25

p, (the probability of success of any one trial) : 0.15

x value (the exact number of successes here): 3

This gives you a value of .217379...

This is the exact result that Jon gave.

For the second problem, there are simply two formulas to use

n = number of attempts.

p = probability of success

q = probability of failure (which is the same as 1 - p):

expected value of a binomial = n * p

standard deviation of a binomial probability = sqrt (n * p * q)

Answer 2

You can apply the binomial probability formula here:

p = 0.15 q = 0.85 n = 25 k = number of successes (were never in museum)

P(k successes) = n! / [ (n-k!) k!] p^k q^(n-k)

1). P(k = 3) = 25!/[22! 3!] 0.15^3 0.85^22 = 0.22

2) mean of binomial distribution = n * p = 25 * 0.15 = 4

standard deviation of binomial distribution = sqrt(n* p * q) = sqrt(25 * 0.15 * 0.85) = 1.79