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Probability Problem Set: Personal Website Hits and Email Use

1. Hits on a personal web site occur quite infrequently. They occur randomly and independently with an average of five per week.
a) Find the probability that the site gets 10 or more hits per week.
b) Determine the probability that the site gets 20 or more hits in two weeks

2. The random variable X is exponentially distributed with sigma = .5. Find the following probabilities.
a) P(X > 1)
b) P(X > .4)
c) P(X < .5)
d) P(X < 2)

3. A factory's worker productivity is normally distributed. One worker (worker 1) produces an average of 75 units per day with a standard deviation of 20. Another worker (worker 2) produces at an average rate of 65 per day with a standard deviation of 21. What is the probability that during one week (5 working days) worker 1 will produce more than worker 2?

4. According to TNS Intersearch, 69% of wireless web users use it primarily for receiving and sending e-mail. Suppose that three wireless web users are selected at random. What is the probability that all of them use it primarily for e-mail?

5.The effects of an antidepressant drug varies from person to person. Suppose that the drug is effective on 89% of women and 65% of men. It is known that 66% of the people who take the drug are women. What is the probability that the drug is effective?

Solution Preview

See the attached file.

1. a. P (x>=10)=1- POISSON.DIST(9,5,TRUE)=1- 0.968172= 0.031828
b. there are more possibilities: 2*(P(x=0)*P(x>=20)+P(x=1)*P(x>=19)+P(x=2)*P(x>=18)+...+P(x=20)*P(x>=0))= 0.006907997

2. a) ...

Solution Summary

This solution provides work and answers in plain text regarding a personal website hits and email use in the attached Excel file. Excel formulas are used and provided for calculations.