Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 240 feet and a standard deviation of 50 feet. Let X = distance in feet for a fly ball.

If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 202 feet? (Round your answer to four decimal places.)

Find the 80th percentile of the distribution of fly balls. (Round your answer to one decimal place.)
               ft

Write the probability statement. (Let k represent the score that corresponds to the 80th percentile.)

P(X < k) =

Answer 1

Solution :

Given that ,

a) P(x < 202)

= P[(x - ) / < (202 - 240) / 50]

= P(z < -0.76)

Using z table,

= 0.2236

b) Using standard normal table,

P(Z < z) = 80%

= P(Z < z ) = 0.80

= P(Z < 0.8416 ) = 0.80  

z = 0.8416

Using z-score formula,

x = z * +

x = 0.8416 * 50 + 240

x = 282.1