The number two is both even and prime. Suppose a card with a two is mixed with seven other even number cards that are not twos. A pair of cards is drawn with replacement.

I understand how to get the number of different samples possible and that is 64.

I understand how to get the number of samples for which the proportion of non-prime even numbers is one and that is 49.

I do not understand how I find the mean of the sampling distribution of the proportion of non-prime even numbers. Although I know the answer is 0.875 I do not understand how you arrive at that. Can you please show me how that is determined?

Solution Preview

There are 8 total cards; one is prime, seven are not prime. You are correct that the number of different possible of pairs of cards is 64 (8 possibilities for card #1, 8 for card #2, 8 x 8 = 64). Similarly there are 49 possible pairs of non-prime cards (7 x 7 = 49).

You want to find the mean of the sampling distribution of the proportion of non-prime cards. For each pair of cards, the proportion ...

Finding Mean, Variance, PMF & Binomial Distribution: Example. 1. A random variable X has a binomial distribution with mean 6 and variance 3.6. Find P(X = 4). ...

Finding probabilities with the help of binomial distribution. A regional manager visits local fast-food franchises and evaluates the speed of the service. ...

... 10. In which of the following binomial distributions is the normal ... 4. Find the mean and standard deviation of the following probability distribution: ...

...Find a 95% confidence interval for the true proportion of all college students who own personal computers. Question 1 If a normal distribution of empirical ...

... Use the Poisson Distribution to find the indicated ... number of calls per hour, find the probability ... computing probability from Binomial and Poisson distributions. ...

... involves finding probabilities for normal and binomial probability distributions. ... Find the mean, variance, and standard deviation for the distribution. ...

... library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the point in the distribution in which ...