Probability Questions
1. A quality control engineer knows that 10% of the microprocessor chips produced by a machine are defective. Out of a large shipment, five chips are chosen at random. What is the probability that none of them is defective? What is the probability that at least one is defective?
2. An automated manufacturing process produces a component with an average width of 7.55 centimeters, with a standard deviation of 0.02 centimeter. All components deviating by more than 0.05 centimeter from the mean must be rejected. What percentage of parts must be rejected? Assume a normal distribution. 3. Assume that the number of cases sold per week in December by a large group of beverage salesmen is quite close to normal distribution with a mean of 684 and a standard deviation of 60.
a. Given that the top 16% of the salesmen receive bonuses, how many cases must a salesman sell in order to receive bonus?
b. If the break-even number of cases is 600 per salesman, what proportions of the salesman are above the break-even value?
4. Neutral Executive Company is conducting an exercise to find out the age of its accounts receivables (i.e. classifying its debtors into how long each debtor is overdue). The data collected indicate that the age of the accounts follows a normal distribution, with = 28 days and = 8 days.
a. What proportion of the accounts is between 20 and 40 days old?
b. The company administrator is interested in sending reminder letters to the oldest 15 % of accounts. How many days old should an account be before a reminder letter is sent?
c. The company administrator would like to give a 5 % discount to those Accounts, which pay their balance by the 21st day. What percentage of the Accounts will receive the discount?
5. An advertisement for AT&T encourages people to make overseas phone calls. The advertisement highlights the average cost per minute of calling time to United Kingdom during “economy time” as 64 cents. An agency wants to test this claim, believing
2. An automated manufacturing process produces a component with an average width of 7.55 centimeters, with a standard deviation of 0.02 centimeter. All components deviating by more than 0.05 centimeter from the mean must be rejected. What percentage of parts must be rejected? Assume a normal distribution. 3. Assume that the number of cases sold per week in December by a large group of beverage salesmen is quite close to normal distribution with a mean of 684 and a standard deviation of 60.
a. Given that the top 16% of the salesmen receive bonuses, how many cases must a salesman sell in order to receive bonus?
b. If the break-even number of cases is 600 per salesman, what proportions of the salesman are above the break-even value?
4. Neutral Executive Company is conducting an exercise to find out the age of its accounts receivables (i.e. classifying its debtors into how long each debtor is overdue). The data collected indicate that the age of the accounts follows a normal distribution, with = 28 days and = 8 days.
a. What proportion of the accounts is between 20 and 40 days old?
b. The company administrator is interested in sending reminder letters to the oldest 15 % of accounts. How many days old should an account be before a reminder letter is sent?
c. The company administrator would like to give a 5 % discount to those Accounts, which pay their balance by the 21st day. What percentage of the Accounts will receive the discount?
5. An advertisement for AT&T encourages people to make overseas phone calls. The advertisement highlights the average cost per minute of calling time to United Kingdom during “economy time” as 64 cents. An agency wants to test this claim, believing