Question

A professional baseball pitcher takes 15.76 seconds to throw each​ pitch, on average. Assume the​ pitcher's times per pitch follow the normal probability distribution with a standard deviation of 2.4 seconds.

a. What is the probability that a random sample of 20 pitches from this pitcher will have a mean less than 15 seconds?

P(x<15)=

b. What is the probability that a random sample of 30 pitches from this pitcher will have a mean less than 15 seconds?

P(x<15)=

c. What is the probability that a random sample of 40 pitches from this pitcher will have a mean less than 15 seconds?

P(x<15)=

Answer 1

Here, mean = 15.76 , sigma = 2.4

a)
n = 20

P(x< 15)
= P(z < (x - mean)/(sigma/sqrt(n))
= P(z< (15 - 15.76)/(2.4/sqrt(20))
= P(z< -1.4162) using z left tailed table,
= 0.0784

b)

n = 30

P(x< 15)
= P(z < (x - mean)/(sigma/sqrt(n))
= P(z< (15 - 15.76)/(2.4/sqrt(30))
= P(z< -1.7345) using z left tailed table
= 0.0414

c)

n = 40

P(x< 15)
= P(z < (x - mean)/(sigma/sqrt(n))
= P(z< (15 - 15.76)/(2.4/sqrt(40))
= P(z< -2.0028) using z left tailed table
= 0.0226