Question

QUESTION 20 5 points Save Answer Use the information below, answer the next 2 questions: Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. (a) What is the probability that the 49 balls traveled an average of less than 240 feet? (Round to 3 decimal places) QUESTION 21 5 points Save Answer (b) Find the 80th percentile of the distribution of the average of 49 fly balls. Click Save and Submit to saue and submit Click Save All Answers to saue all answers

Answer 1

Solution :

Given that ,

mean = $\mu$ = 250

standard deviation = $\sigma$ = 50

n = 49

$\mu$_{$\bar x$} = 250

$\sigma$_{$\bar x$} =$\sigma$  / $\sqrt$ n = 50 / $\sqrt$ 49=7.14

P($\bar x$ < 240) = P[($\bar x$ - $\mu$ _{$\bar x$} ) / $\sigma$ _{$\bar x$} < (240-250 / 7.14]

= P(z < -1.40)

Using z table

= 0.0808

=0.081

B.

ng standard normal table,

P(Z < z) = 80%

= P(Z < z) = 0.80  

= P(Z < ) = 0.80

z = 0.84

Using z-score formula  

$\bar x$ = z * $\sigma$ _{$\bar x$}+ $\mu$ _{$\bar x$}

$\bar x$ = 0.84 *7.14+250

=256