Question

A professional baseball pitcher takes 14.76 seconds to throw each pitch, on average. Assume the pitcher's times per pitch follow the normal probability distribution with a standard deviation of 2.2 seconds. Complete parts a through c.

a). What is the probability that a random sample of 10 pitches from this pitcher will have a mean less than 14 seconds?

P(x< 14) =

b). What is the probability that a random sample of 30 pitches from this pitcher will have a mean less than 14 seconds?

P(x<14)=

c). What is the probability that a random sample of 50 pitches from this pitcher will have a mean less than 14 seconds?

P(x<14)=

Answer 1

Solution :

Given that ,

mean = = 14.76

standard deviation = = 2.2

a) n = 10

= = 14.76

= / n = 2.2/ 10 = 0.6957

P( < 14) = P(( - ) / < (14 -14.76) /0.6957 )

= P(z < -1.09 )

= 0.1379

probability = 0.1379

b)

n = 30

= = 14.76

= / n = 2.2/ 30 = 0.4017

P( < 14) = P(( - ) / < (14 -14.76) /0.4017 )

= P(z < -1.89 )

= 0.0294

probability = 0.0294

c)

n = 50

= = 14.76

= / n = 2.2/ 50 = 0.3111

P( < 14) = P(( - ) / < (14 -14.76) /0.3111 )

= P(z < -2.44 )

= 0.0073

probability = 0.0073