Question

A. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

? = 6; ? = 2

P(5 ? x ? 8) =

B. Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

? = 13.8; ? = 3.1

P(8 ? x ? 12) =

C.Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

? = 18; ? = 4.2

P(x ? 30) =

Answer 1

A:

Here we have

The z-score for X = 5 is

The z-score for X = 8 is

The required probability is

P(5<X<8) = P(-0.5<z<1) = 0.5328

The excel function used for finding probability is "=NORMSDIST(1)-NORMSDIST(-0.5)".

B:

Here we have

The z-score for X = 8 is

The z-score for X = 12 is

The required probability is

P(8<X<12) = P(-1.87<z<-0.58) = 0.2502

The excel function used for finding probability is "=NORMSDIST(-0.58)-NORMSDIST(-1.87)".

C)

Here we have

The z-score for X = 30 is

The required probability is

P(X>30) = P(z>2.86) = 0.0021

The excel function used for finding probability is "=1-NORMSDIST(2.86)".