Question

Use Minitab to compute each of the following. Be sure to INCLUDE the commands from the Session Window so that I can determine “how” you obtained your answers.

I will NOT grant credit for problems that do not include the commands from the session window!

1. In 2009 it was reported that 78% of all Americans had a computer in their home. Suppose we take a random sample of 100 American homes and let X be the number which own a computer.

a. Find the probability that at least 60 homes own a computer.

b. Why do you think your answer to part ‘a’ came out the way it did?

c. Find the probability that less than 60 owned a computer.

d. Could you have used the answer from part (a) to answer part (c)? How?

Answer 1

Solution:-

a) The probability that at least 60 homes own a computer is 0.999985.

n = 100, p = 0.78

x = 60

P(x > 60) = 0.999985

To compute the probability of at least 60 successes, select Calc > Probability Distributions > Binomial..

fx Calculator... Column Statistics... Row Statistics.. A Standardize... Make Patterned Data H Make Mesh Data... Make Indicator Variables... Set Base... Random Data Probability Distributions Matrices Chi-Square... Normal... F... t... Uniform... Binomial... Geometric... Probability Distributions - Binomial Negative Binomial... Calculate the PDF, CDF, or inverse CDF for a binomial Hypergeometric... distribution Discrete...

For this question we need to choose Inverse cumulative probability.

Minitab output:

Inverse Cumulative distribution Function:

Binomial with n = 100 and p = 0.78

x P(X > x)

60 0.999985

b) The expected number of Americans having a computer in their home is 78. If we calculate the probability of at least 60, that will be almost equal to 1.

c) The probability that less than 60 owned a computer is 0.000015.

P(x < 60) = P(x < 60) - P(x = 60)

P(x < 60) = 0.000038 - 0.000023

P(x < 60) = 0.000015

For this question first we need to choose cumulative probability and then probability. All the inputs will remain the same as in the previous part

Minitab output:

Cumulative distribution Function:

Binomial with n = 100 and p = 0.78

x P(X < x)

60 0.000038

Probability distribution Function:

Binomial with n = 100 and p = 0.78

x P(X = x)

60 0.000023

d)

P(x < 60) = 1 - P(x > 60)

P(x < 60) = 1 - 0.999985

P(x < 60) = 0.000015