Question

With a mean of 92.12

and a standard deviation of 2.43

Finding Values: A baseball fan wishes to identify the fastballs among the fastest 20% of all such pitches. Above what speed must a fastball be in order to be included in the fastest 20%? Round your answer to the nearest 0.1 mph.

Answer 1

Solution:-

Given that,

mean = = 92.12

standard deviation = = 2.43

Using standard normal table,

P(Z > z) = 20%

= 1 - P(Z < z) = 0.20

= P(Z < z) = 1 - 0.20

= P(Z < z ) = 0.80

= P(Z < 0.84 ) = 0.80

z = 0.84 ( using z table )

Using z-score formula,

x = z * +

x = 0.84 * 2.43+92.12

x =94.16

x=94.2