# Category Archives: Statistics

## What is the probability that the parcel was shipped express and arrived the next day?

1.  In a lot of n components, 30% are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. For which lot size n will A and B be more nearly independent: n = 10 or n = 10,000? Explain.

2.  A certain delivery service offers both express and standard delivery. Seventy-five percent of parcels are sent by standard delivery, and 25% are sent by express. Of those sent standard, 80% arrive the next day, and of those sent express, 95% arrive the next day. A record of a parcel delivery is chosen at random from the company’s files.

a.  What is the….

## Given that the test is positive, what is the probability that the person has the disease?

1.  Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw.

a.  Assume that the probability that an item has a flaw is 0.10. If an item is passed by the first inspector, what is the probability that it actually has aflaw?

b.   Assume that the probability that an item has a flaw is 0.10. If an item is passed by both inspectors, what is the probability that it actually has a flaw?

2.   Refer to Example 2.26. Assume that the proportion of people in the community who have the disease is 0.05.

a.   Given that the test is positive, what is the probability that the person has the disease?

….

## If a man tests negative, what is the probability that he actually has the disease?

1.  Refer to Example 2.26.

a.  If a man tests negative, what is the probability that he actually has the disease?

b.  For many medical tests, it is standard procedure to repeat the test when a positive signal is given. If repeated tests are independent, what is the probability that a man will test positive on two successive tests if he has the disease?

c.   Assuming repeated tests are independent, what is the probability that a man tests positive on two successive tests if he does not have the disease?

d.  If a man tests positive on two successive tests, what is the probability that he has the disease?

2.  If A and B are independent events, prove that the following pairs of events are independent: A c and B,….

## Find the probability mass function of X

1.  Determine whether each of the following random variables is discrete or continuous.

a.  The number of heads in 100 tosses of a coin.

b.  The length of a rod randomly chosen from a day's production.

c.   The final exam score of a randomly chosen student from last semester's engineering statistics class.

d.  The age of a randomly chosen Colorado School of Mines student.

e.  The age that a randomly chosen Colorado School of Mines student will be on his or her next birthday.

2.   A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had 5. Let X represent the number of occupants in a….

## What is the smallest possible value for Y?

1.   Candidates for a job are interviewed one by one until a qualified candidate is found. Thirty percent of the candidates are qualified.

a.  What is the probability that the first candidate is qualified?

b.  What is the probability that the first candidate is unqualified and the second candidate is qualified?

c.   Let X represent the number of candidates interviewed up to and including the first qualified candidate.

d.  Find P(X = 4). Find the probability mass function of X.

2.   Refer to Exercise 10. The company has two positions open. They will interview candidates until two qualified candidates are found. Let Y be the number of candidates interviewed up to and including the second qualified candidate.

a.  What is the smallest possible value for Y?

b.  What is….