1. A.K Stryker is an outstanding soccer player. He scores on 30% of his shots at

Question

1. A.K Stryker is an outstanding soccer player. He scores on 30% of his shots attempted. Let X be the random variable defined as the number of goals scored on 50 attempts. Jim Bluffum is a renowned blackjack player. He wins 25% of the time. The random variable Y is defined as the number of games needed to win his first game. The random variable Z is defined as the total number of soocer goals scored and the number of blackjack games played. Determine the mean and standard deviation of the random variable Z.

Select one:

a. 11, 3.28

b. 11, 4.74

c. 19, 3.28

d. 19, 4.74

e. Not enough information given to determine the mean and standard deviation

2. A probability experiment involves a series of identical, independent trials with two outcomes (success/failure) per trial and the probability of success on each trial is 0.1. Determine the number of trials, n, in a binomial experiment such that the expected number of successes in that binomial experiment will be equal to the expected number of trials ina geometric experiment.

Select one:

a. 2

b. 5

c. 10

d. 50

e. 100

Explanation / Answer

For the random variable Z = X + Y

Mean(Z) = Mean(X) + Mean(Y)

Var(Z) = Var(X) + Var(Y)

X = bin ( 50, 0.30)

mean(X) = np = 50 * 0.30 = 15

Average number of games to be played by Y to get one success = 4

Hence, Mean(Z) = 15 + 4 = 19

Var(X) = sqrt( 50 * 0.30 * 0.70) = 3.24

Var(Y) = 0 since it is a fixed number.

Hence, option C is correct.

2)

Expected number of trials for a binomial distribution = np = n * 0.1

Expected number of trials before success in a geometric experiment = 1 / p = 1/ 0.1 = 10

Thus,

10 = 0.1n

n = 100

Hope this helps.

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