If you have a sample with mean 100 and standard deviation 22

If you have a sample with mean 100 and standard deviation 22, what is the probability that x = 75?(assuming a normal distribution) (round to 2 decimal places)

Solution

If you have a sample with mean 100 and standard deviation 22, what is the probability that x = 75?(assuming a normal distribution) (round to 2 decimal places)

Assuming continuity correction

P( x=75) = p( 74.5<x<75.5)

Z value for 74.5, z=(74.5-100)/22 = -1.16

Z value for 75.5, z=(75.5-100)/22 = -1.11

P( -1.16<z<-1.11) = P( z< -1.11)