Question

The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of 2.75 inches and a standard deviation of 0.04 inch. A random sample of 10 tennis balls is selected. What is the probability that the sample mean is less than 2.74 ​inches?

Answer 1

Solution :

Given that ,

mean = = 2.75 inches

standard deviation = = 0.04 inch

n = 10

= 2.75 and

= / n = 0.04 / 10 = 0.01

P( <2.74 ) = P(( - ) / < ( 2.74 - 2.75 ) / 0.01)

= P(z < -1 )

= 0.1587 Using standard normal z table,

P( < 2.74) = 0.1587