Exam 4: Discrete Random Variables

A lab orders a shipment of 100 frogs each week. Prices for the weekly shipments of frogs follow the distribution below: Price \ 10.00 \ 12.50 \ 15.00 Probability 0.25 0.4 0.35 How much should the lab budget for next yearʹs frog orders assuming this distribution does not Change? (Hint: Find the expected price and assume 52 weeks per year.)

Mamma Temte bakes six pies each day at a cost of $2 each. On 31% of the days she sells only two pies. On 18% of the days, she sells 4 pies, and on the remaining 51% of the days, she sells all six Pies. If Mama Temte sells her pies for $4 each, what is her expected profit for a dayʹs worth of pies? [Assume that any leftover pies are given away.]

The conditions for both the hypergeometric and the binomial random variables require that the trials are independent.

The hypergeometric random variable x counts the number of successes in the draw of 3 elements from a set of 8 elements containing 4 successes. List the possible values of x.

Solve the problem. Round to four decimal places. -If x is a binomial random variable, compute p(x)for n = 6, x = 2, p = 0.6.

The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 4. Find the probability that exactly three road construction Projects are currently taking place in this city.

A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability for the value of x = 5. 2 3 5 8 10 () 0.10 0.20 ??? 0.30 0.10

A discrete random variable x can assume five possible values: 2, 3, 5, 8, 10. Its probability distribution is shown below. Find the probability that the random variable x is a value greater Than 5. 2 3 5 8 10 p(x) 0.10 0.20 0.30 0.30 0.10

You test 3 items from a lot of 12. What is the probability that you will test no defective items if the lot contains 2 defective items?

Consider the given discrete probability distribution. Find P(x<2 or x>3) . x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2

If $\mathrm { x }$ is a binomial random variable, calculate $\sigma ^ { 2 }$ for $\mathrm { n } = 40$ and $\mathrm { p } = 0.7$ .

Suppose $x$ is a random variable for which a Poisson probability distribution with $\lambda = 3$ provides a good approximation. a. Graph $p ( x )$ for $x = 0,1,2,3,4,5,6$ . b. Find $\mu$ and $\sigma$ for $x$ . c. What is the probability that $x$ will fall in the interval $\mu \frac { \circ } { \sigma }$ ?

A coin is flipped 6 times. The variable x represents the number of tails obtained. List the possible values of x. Is x discrete or continuous? Explain.

Classify the following random variable according to whether it is discrete or continuous. The number of phone calls to the attendance office of a high school on any given school day

Consider the given discrete probability distribution. Find $P ( x \leq 4 )$ . x 0 1 2 3 4 5 p(x) .30 .25 .20 .15 .05 .05

Given that x is a hypergeometric random variable, compute p(x)for N = 6, n = 3, r = 3, and x = 1.

A local bakery has determined a probability distribution for the number of cheesecakes it sells in a given day. The distribution is as follows: Number sold in a day 0 5 10 15 20 Prob (Number sold) 0.21 0.16 0.1 0.24 0.29 Find the number of cheesecakes that this local bakery expects to sell in a day.

If $\mathrm { x }$ is a binomial random variable, calculate $\sigma$ for $\mathrm { n } = 60$ and $\mathrm { p } = 0.7$ . Round to three decimal places when necessary.

Solve the problem. Round to four decimal places. -According to a recent study, 1 in every 10 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty-five women and Asked each whether she has been a victim of domestic abuse at some point in her life. Find the Probability that more than 22 of the women sampled have not been the victim of domestic abuse.

The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 10 elements containing 2 successes. List the possible values of x.