The diameter of a brand of pingpong balls is approximately n

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 4 ping-pong balls is selected. Complete parts (a) through (d). What is the sampling distribution of the mean? What is the probability that the sample mean is less than 1.27 inches?

Solution

Standard error = sd/sqrt(n) = 0.04/sqrt(4) =0.02

Z value for 1.27, z=(1.27-1.31)/ 0.02 = -2

P( mean x < 1.27)

= P( z < -2)

= 0.0228