# Probability

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1) A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.

A) Compute the probability that a randomly selected household has a savings account.

B) Compute the probability that a randomly selected household has no checking account and no savings account.

C) Compute the probability that a randomly selected household with a savings account has no checking account.

2) A study of Brand M washing machines that failed within three years (warranty period) was 23.2%. Of those that failed, 82.9% lasted over two years. What is the probability that a washer which lasts at least two years will still fail before the end of the warranty period?

3) In an office suite there are three electric typewriters available for personnel to use other than secretaries. Since no one person uses these typewriters, maintenance is not as frequent as for other typewriters. The probability that any one of these typewriters is able to function is 0.90. A mailroom clerk has a form to be filled out and is to type it. It can be typed if any one of the three typewriters operate. Find the probability that at least two of the machines will operate at a given time.

4) New York City is estimated to have 21 percent of the homes with T.V. sets served by cable T.V. If a random sample of four is taken from these homes find the probability distribution of x where x is the number of T.V. homes in the sample having cable T.V. What is the probability that:

a) All four T.V. homes in the sample are served by cable.

b) At least one T.V. home in the sample is served by cable.

c) Compute the mean and standard deviation of the number of T.V. homes with cable service in the sample.

5) In a takeover bid for a certain company, management of the raiding firm believes that the takeover has a 0.65 probability of success if a member of the board of the raided firm resigns, and a 0.30 probability of success if she does not resign. Management of the raiding firm believes that the chances for a resignation of the member in question are 0.70.

a) What is the probability of a successful takeover?

b) Assuming a takeover was not successful, what was the probability that the board member resigned?

6) Which of the following might have resulted from poor sampling design? (Choose only ONE BEST ANSWER)

a. The respondents misrepresented their level of income.

b. The respondents omitted reporting illegal income.

c. The sample failed to include a representative portion of minorities.

d. In a random sample of residents of New York City, 90% of the sample indicated that they were Democrats.

e. The sample was not randomly selected.

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##### Solution Summary

1) A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 79.3% had savings accounts.

A) Compute the probability that a randomly selected household has a savings account.

B) Compute the probability that a randomly selected household has no checking account and no savings account.

C) Compute the probability that a randomly selected household with a savings account has no checking account.

2) A study of Brand M washing machines that failed within three years (warranty period) was 23.2%. Of those that failed, 82.9% lasted over two years. What is the probability that a washer which lasts at least two years will still fail before the end of the warranty period?

3) In an office suite there are three electric typewriters available for personnel to use other than secretaries. Since no one person uses these typewriters, maintenance is not as frequent as for other typewriters. The probability that any one of these typewriters is able to function is 0.90. A mailroom clerk has a form to be filled out and is to type it. It can be typed if any one of the three typewriters operate. Find the probability that at least two of the machines will operate at a given time.

4) New York City is estimated to have 21 percent of the homes with T.V. sets served by cable T.V. If a random sample of four is taken from these homes find the probability distribution of x where x is the number of T.V. homes in the sample having cable T.V. What is the probability that:

a) All four T.V. homes in the sample are served by cable.

b) At least one T.V. home in the sample is served by cable.

c) Compute the mean and standard deviation of the number of T.V. homes with cable service in the sample.

5) In a takeover bid for a certain company, management of the raiding firm believes that the takeover has a 0.65 probability of success if a member of the board of the raided firm resigns, and a 0.30 probability of success if she does not resign. Management of the raiding firm believes that the chances for a resignation of the member in question are 0.70.

a) What is the probability of a successful takeover?

b) Assuming a takeover was not successful, what was the probability that the board member resigned?

6) Which of the following might have resulted from poor sampling design? (Choose only ONE BEST ANSWER)

a. The respondents misrepresented their level of income.

b. The respondents omitted reporting illegal income.

c. The sample failed to include a representative portion of minorities.

d. In a random sample of residents of New York City, 90% of the sample indicated that they were Democrats.

e. The sample was not randomly selected.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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