A normal distribution has a mean of 50 and a standard deviat

A normal distribution has a mean of 50 and a standard deviation of 6. What is the probability that a value selected at random from this data is in the interval from 38 to 56? Express your answer as a percent rounded to the nearest tenth.

A) 79.5%

B) 81.5%

C) 85%

D) 90%

Solution

z scores : z1 = (38 - 50)/6 = -12/6 = -2

z2 = (56 -50)/6 = 1

probability that a value selected at random from this data is in the interval from 38 to 56

P(z1< z< z2) : Use the standard normal table to conclude that:

P( -2<z<1) = 0.8185 = 81.8

Option B nearest answer