Suppose X is a discrete random variable with probability distribution as given in the table below.
In a quarter-pound bag of red pistachio nuts, some shells are too difficult to pry open by hand. Suppose the random variable X, the number of pistachios in a randomly selected bag that cannot be opened by hand, has the probability distribution given in the table below.
a. Is this a valid probability distribution? Justify your answer.
b. Find the mean, variance, and standard deviation of X.
c. Find the probability X takes on a value less than the mean.
d. Suppose two bags of pistachios are selected at random. What is the probability that both bags have four or more pistachios too difficult to open by hand?
Suppose the number of rides that a visitor enjoyed at Disney World during a day is a random variable with probability distribution given in the table below.
a. Find the mean number of rides for a Disney World visitor.
b. Find the variance and standard deviation of the number of rides for a Disney World visitor.
c. Find the probability that the number of rides for a randomly selected Disney World visitor is within one standard deviation of the mean. Write a Solution Trail for this problem.
d. Find the probability that the number of rides for a randomly selected Disney World visitor is less than one standard deviation above the mean.