# 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.

12 Multiple Choice Word Problems involving the Binomial, Normal, Poisson and Exponential Probability Distributions

Need some assistance with the following questions.

Please provide your answers and supporting documentation in excel format for the following questions.The answers in excel should match the options provided.

A student has an important exam coming up and is contemplating not studying for the exam in order to attend a party with his friends. The student must earn a minimum score of 70% on the exam in order to successfully maintain his desired GPA. Suppose the student knows in advance that the exam will consist of twenty multiple choice questions with four possible answers for each question. Answer questions 1-3 using the preceding information and modeling this situation as a binomial distribution.

1. What is the probability that the student will successfully earn exactly the required minimum score of 70% on the exam based solely upon randomly guessing the correct answer for each question?

o 2.57

o 2.57E-02

o 2.57E-05

o 2.57E-04

2. What is the probability that the student will earn less than the required minimum score of 70% on the exam based solely upon randomly guessing the correct answer for each question?

o 0.74673

o 0.85198

o 0.99997

o 0.23499

3. What is the probability that the student will successfully earn no less than the required minimum score of 70% on the exam based solely upon randomly guessing the correct answer for each question?

o 3.51E-04

o 2.95E-05

o 6.87E-06

o 1.27E-03

The mean time required to complete a certain type of construction project is 52 weeks with a standard deviation of 3 weeks. Answer questions 4-7 using the preceding information and modeling this situation as a normal distribution.

4. What is the probability of the completing the project in no more than 52 weeks?

o 0.25

o 0.50

o 0.75

o 0.05

5. What is the probability of the completing the project in more than 55 weeks?

o 0.2743

o 0.5091

o 0.7511

o 0.0546

6. What is the probability of completing the project between 56 weeks and 64 weeks?

o 0.2587

o 0.3334

o 0.5876

o 0.0911

7. What is the probability of completing the project within plus or minus one standard deviation of the mean?

o 0.951

o 0.852

o 0.759

o 0.683

Customers arrive at a supermarket check-out counter with an average arrival rate of 9 customers per hour. Answer questions 8-10 using the preceding information and modeling this situation as a Poisson distribution.

8. What is the probability of less than 5 customers arriving at the supermarket check-out counter in a given one hour period?

o 0.054

o 0.446

o 0.359

o 0.612

9. What is the probability of exactly 12 customers arriving at the supermarket check-out counter in a given one hour period?

o 0.262

o 0.044

o 0.073

o 0.189

10. What is the probability of no less than 12 customers arriving at the supermarket check-out counter in a given one hour period?

o 0.115

o 0.197

o 0.381

o 0.686

A local commuter bus service advertises that buses run every twelve minutes along a certain route. Answer questions 11and 12 using the preceding information and modeling this situation as an exponential distribution.

11. What is the probability of a bus picking up the passengers at a given bus stop in less than or equal to 12 minutes following their arrival at the bus stop?

o 0.519

o 0.632

o 0.466

o 0.772

12. What is the probability of a bus picking up the passengers at a given bus stop in more than 15 minutes following their arrival at the bus stop?

o 0.287

o 0.343

o 0.541

o 0.119