# Normal Distribution- probability calculations using Excel

USE EXCEL TO SOLVE THE FOLLOWING PROBLEMS

PROBLEM 9.13:

The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches.

(a) What is the probability that a randomly selected woman is taller than 66 inches?

(b) A random sample of four women is selected. What is the probability that the sample mean height is greater than 66 inches?

(c) What is the probability that the mean height of a random sample of 100 women is greater than 66 inches?

PROBLEM 9.14

Refer to Exercise 9.13. If the population of women's heights is not normally distributed, which, if any, of the questions can you answer? Explain.

Exercise 9.13: The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches.

(a) What is the probability that a randomly selected woman is taller than 66 inches?

(b) A random sample of four women is selected. What is the probability that the sample mean height is greater than 66 inches?

(c) What is the probability that the mean height of a random sample of 100 women is greater than 66 inches?

[PLEASE SEE THE EXCEL SPREAD SHEET ATTACHED TO HELP WITHA SOLUTION]

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USE EXCEL TO SOLVE THE FOLLOWING PROBLEMS:

PROBLEM 9.13: The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches.

(a) What is the probability that a randomly selected woman is taller than 66 inches?

Probability for x

Mean=M = 64 inches

Standard deviation =s= 2 inches

x= 66

z=(x-M )/s= 1 =(66-64)/2

Cumulative Probability corresponding to z= 1 is= 0.8413

Or Probability corresponding to x< 66.00 is Prob(Z)= 0.8413 0r= 84.13%

Therefore probability corresponding to x> 66.00 is 1-Prob(Z)= 0.1587 =1-0.8413

0r= 15.87%

Answer: 0.1587 or 15.87%

Note: Cumulative probability for x=66 is calculated using EXCEL worksheet function NORMDIST

0.8413 =NORMDIST(66,64,2,1)

The format for NORMDIST worksheet function is

NORMDIST(x,mean,standard_dev,cumulative)

cumulative =1 when we want the probability of x<= 66

(b) A random sample of four women is selected. What is the probability that the sample mean ...

#### Solution Summary

Uses Excel for calculating probabilities in a Normal Distribution.