## Question

1. Determine if the following random variables discrete or continuous:

a. Number of fish I caught during 2 hours.

b. Temperature of a coffee cup.

c. Height of a 2-year-old maple tree

d. Number of credit cards I have in my wallet

e. The number of days until your next birthday.

2. Thickness of wood panels can be ordered in 1/8, 1/4, 1/2 inches. The probability that a panel is ordered in 1/8, ¼, and ½ inches are 0.5, 0.3, and 0.2 respectively. Let the random variable X be the total thickness of 2 ordered wood panels.

a. Determine the range of X

b. Determine the probability mass function of X.

c. Find the mean and variance of X.

d. Find P(X < ½)

3. Neuroblastoma, a rare form of malignant tumor, occurs in 11 children in a million, so its probability is 0.000011. Four cases of neuroblastoma occurred in Oak Park, Illinois, which had 12,429 children.

a. Assuming that neuroblastoma occurs as usual, find the mean and standard deviation of cases in groups of 12,429 children.

b. Find the probability that the number of neuroblastoma cases in a group of 12,429 children is 0 or 1.

c. Does the cluster of four cases in Oak Park, Illinois, appear to be attributable to random chance? Why or why not?

4. On average, 70 percent of the passengers on a flight from San Francisco to Boston prefer chicken to fish. Assume that the passengers have only one of two choices, chicken or fish for their meal. If there are 200 passengers on a flight and the airline carries 140 chickens and 60 fish dinners, what is the probability that more than five passengers will be disappointed?

5. The number of geysers emitted from the ground follows Poisson distribution with the mean rate of 3 per day.

a. Find the probability that there is at least one emission during 12-hour period.

b. How many emissions can be expected in 12-hour period?

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