Suppose that 𝑋 is normally distributed with mean 85 and standard deviation 19. A. What is the probability that 𝑋 is greater than 114.07?

Question

Suppose that 𝑋X is normally distributed with mean 85 and standard deviation 19.

What is the probability that 𝑋X is greater than 114.07?

Answer 1

Calculate (114.07 − 85) ÷ 19 to obtain a z-value of 1.53.

Corresponding proportion of area under the standard

normal curve for z = 1.53 is given by calculator program

as 0.4369916355.

Then P(X > 114.07) is obtained by 1 − (0.4369916355 + 0.5)

or 0.06300836447, equivalent to 0.0630.

A table of values gives the proportion of area for z = 1.53 as 0.4370;

then 1 − (0.4370 + 0.5) gives 0.0630 as above.