Question

1.

A football team consists of 18 freshmen and 18 sophomores, 15 juniors, and 12 seniors.

Four players are selected at random to serve as captains. Find the probability that at least 1 of the students is a senior.

2.

If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of

three, he wins $20. The cost to play the game is $5. What is the expectation of this game?

3.

Determine the indicated probability for a binomial experiment with the given number of

trials n and the given success probability p.

n=13, p=0.7, P(Fewer than 4)

4.

The Australian sheep dog is a breed renowned for its intelligence and work ethic. It is

estimated that 45% of adult Australian sheep dogs weigh 65 pounds or more. A sample of 18 adult dogs is studied. What is the standard deviation of the number of dogs who weigh 65 lb or more?

5.

If there are 20 typographical errors randomly distributed in a 250-page document, find

the probability that a given page contains exactly two errors.

6.

Last year, a manufacturer produced 1,850,000 DVD players. Of these, approximately 2%

were defective. Assume that a simple random sample of n=220 players is drawn. Use the Poisson approximation to the binomial distribution to compute the probability that exactly fourteen of the 220 DVD players were defective.

7.

The average charitable contribution itemized per income tax return in Pennsylvania is

$792. Suppose that the distribution of contributions is normal with a standard deviation of $103. Find the limits for the middle 50% of contributions

8.

X is a normally distributed random variable with a standard deviation of 3.00. Find the

mean of Xif 12.71% of the area under the distribution curve lies to the right of 11.42. (Note: the diagram is not necessarily to scale.)

ment

9.

A sample of size 36 will be drawn from a population with mean 27 and standard

deviation 13. Find the probability that x will be greater than 30.

10.

A ferry will safely accommodate 70 tons of passenger cars. Assume that the mean weight 17)

of a passenger car is 1.7 tons with standard deviation 0.7 tons. If a random sample of 37 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded?

11.

A ferry will safely accommodate 82 tons of passenger cars. Assume that the mean weight

of a passenger car is 1.9 tons with standard deviation 0.6 tons. If a random sample of 40 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded?

12.

Use the normal approximation to find the indicated probability. The sample size is n, the

population proportion of successes is p, and X is the number of successes in the sample.

n=90, p=0.53: P(X<50)

13.

A biologist estimates that 40% of the deer in a region carry a certain type of tick. For a

sample of 300 deer selected at random, what is the chance that 124 or fewer deer have this tick?

Answer 1

1:

Total number of players

18+15+12 = 45

Number of ways of selecting 4 players out of 45 is C(45, 4).

Number of players excluding seniors is = 45 - 12 = 33

The number of ways of selecting players not including any senior is C(33,4).

The probability that out of 4 players no senior is selected is

P(no senior) = C(33, 4) / C(45, 4)

The probability that at least 1 of the students is a senior is

Answer: 0.7254

(2)

Let X is a random variable shows the winning amount.

Here X can take values $10-$5 = $5, $20-$5 = $15 and -$5.

Following is the possible outcomes when we sum the outocmes of two rolls of die:

Out of 36 outcomes, 3 outcomes shows sum 10 so

P(X = $5) = 3/36

Out of 36 outcomes, 2 outcomes shows sum 3 so

P(X = $15) = 2 /36

By the complement rule,

P(X= -$5) = 1 - (3/36) - (2/36) = 31 / 36

The expected value is

E(X) = P(X = $5) * 5 + P(X = $15) * 15 + P(X= -$5) *(-5) = 5 * (3/36) + 15 * (2/36) - 5 * (31 / 36) = -110/ 36 = -$3.06

Answer : -$3.06