State any assumptions necessary to do the following problems. Unless otherwise stated, conduct all hypothesis tests at the five percent significance level.
1. A lottery ticket costs $1 and each winning ticket will receive $5 million. The probability of winning is one in ten million.
a. Find the expected winnings and standard deviation for each lottery ticket sold.
b. If 20 million tickets are sold, find the probability that there will be
i) exactly three winners.
ii) more than five winners.
c. If 250 million tickets are sold what is the probability that there will be between 20 and 28 winners?
2. Find the probability of getting 70% or better on a 15-question, True-False test if you are “clueless”.
3. a. Find the mean and standard deviation of the following random variable:
|
X |
P(X) |
|
|
|
|
0 |
.05 |
|
|
|
|
1 |
.10 |
|
|
|
|
2 |
.40 |
|
|
|
|
3 |
.30 |
|
|
|
|
4 |
.15 |
|
|
|
|
|
|
|
|
|
b. What is the probability that a value drawn from this population exceeds 2.3?
c. What is the probability that the mean of a random sample of 100 values drawn from this population exceeds 2.3?
4. A
survey of 100 Citadel Alumni found that eighteen favored the admission of women
to their alma mater. Can one conclude,
at the ten percent significance level, that fewer than 25 percent of the alumni
are in favor of admitting women?
5. If a
random sample of 16 Fortune 500 CEO's found a mean compensation of $835,000 and
a standard deviation of $340,000, construct a 99% confidence interval for the
population mean compensation for Fortune 500 CEOs.