Question

The diameter of a brand of​ ping-pong balls is approximately normally​ distributed, with a mean of 1.31 inches and a standard deviation of 0.04 inch. A random sample of 16 ​ping-pong balls is selected. Complete parts​ (a) through​ (d). What is the probability that the sample is between 1.28 and 1.3 ​inches?

Answer 1

Solution :

Given that,

mean = = 1.31

standard deviation = = 0.04

n=16

= 1.31

=  / n = 0.04 / 16=0.01

= P(1.28<    < 1.3) = P[(1.28-1.31) /0.01 < ( - ) / < (1.3-1.31 / 0.01)]

= P( -3< Z < -1)

= P(Z <-1 ) - P(Z <-3 )

Using z table,  

= 0.1587-0.0013

= 0.1574