Question

2. A sports company manufactures baseball bats. Before baseball bats are shipped to retailers, some are randomly selected and subjected to the “Smash Test”. To pass the Smash Test, a bat must endure several collisions with baseballs travelling 100 mph without shattering into pieces. Assume that the probability a randomly selected baseball bat passes the test equals .90, and that consecutive tests are independent of each other. Suppose 16 bats are randomly selected to take the test. Let Y = the number of bats out of 16 that pass the test.

(a) What kind of random variable is Y? Identify the values of any relevant parameters, such as the sample size.

(b) What is the probability that exactly 14 of the 16 bats pass the test?

(c) What is the expected number and standard deviation of bats passing the test?

Answer 1

(a)

Y is a Binomial random variable

Binomial distribution has probability mass function as :

n = Number of trials

p = Probability of success

x = Number of success

In our case,

n = 16

p = Probability that a randomly selected baseball bat passes the test = 0.90

(b)

Probability that exactly 14 of the 16 bats pass the test = P(X=14)

Factorial of n is given as :

Probability that exactly 14 of the 16 bats pass the test = 0.2745

(c)

Expected number of bats passing the test = n*p = 16*(0.90) = 14.4

Standard deviation of bats passing the test =