Determine whether each random variable, x, is discrete or continuous.

i) the number of quarterbacks currently playing in the NFL
ii) the current ages of the quarterbacks

Given the following is a probability distribution of a random variable, x, determine P(x = 3).

The discrete random variable, x, is the number of students absent from class, and f is the number of classes.

Determine the probabilities associated with the values of x: 0, 1, 2, 3, 4.

The discrete random variable, x, is the number of students absent from class, and f is the number of classes.

Find the probability that at least two students are absent for a randomly chosen class.

Find the mean number of students absent from a class. Find the variance.

There are ten marbles in a box: one red, three yellow, and six blue. You are given one pick from the box for 75 cents. You win $5 if you pick a red marble, $1 if you pick a yellow marble, and nothing if you pick a blue marble. If you play the game once, what is your expected net gain?

If you play the game described in question 6 one time, what is the probability that you win (not net) at least one dollar?

At a certain hospital, 32% of its diabetic patients seek care for a kidney-related problem. Decide which probability distribution (binomial, geometric, or Poisson) applies to each of the following.

i) What is the probability that the first diabetic patient needing kidney-related care is the fifth diabetic patient seen at that hospital on a given day?

ii) If the mean number of diabetic patients seeking care for a kidney-related problem a day is 18, what is the probability that there will be 10 such patients tomorrow?

iii) If 50 diabetic patients are randomly chosen from this hospital, what is the probability that less than half of them are seeking care for a kidney-related problem?

Find the probability of having exactly four girls in seven births. Assume no multiple births and that male and female births are equally likely and independent.

Research shows that 72% of consumers have heard of MBI computers. A survey of 500 randomly selected consumers is to be conducted. What is the mean and standard deviation for the number of consumers that have heard of MBI computers?

Suppose that 20% of the M & M’s made by Mars, Inc. are red.

What is the probability that in a sample of 50 randomly selected M & M’s, exactly 15 are red?

Suppose that 20% of the M & M’s made by Mars, Inc. are red.

If, on average, there are 10 red M &M’s per large bag, what is the probability that the next large bag will contain exactly 15 red ones?

Suppose that 20% of the M & M’s made by Mars, Inc. are red.

If you pick M & M’s at random, what is the probability that the first red one picked is the fifteenth M & M you picked?

The odds in favor of picking the number that the ball lands on in roulette are 1:37. What is the probability that you do not pick the correct number until the fifth try?

Suppose the Jacksonville Jaguars fumble, on average, 32 times a season. What is the probability that they will fumble only 16 times next season?