Exam 4: Discrete Random Variables

Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac)from the local paint store in order to paint his motherʹs house. Unknown to the man, three of these cans contains An incorrect mix of paint. For this weekendʹs big project, the man randomly selects four of these 1-gallon cans to paint his motherʹs living room. Let x = the number of the paint cans selected that Are defective. Unknown to the man, x follows a hypergeometric distribution. Find the standard Deviation of this distribution.

The hypergeometric random variable x counts the number of successes in the draw of 5 elements from a set of 12 elements containing 7 successes. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all possible values of x.

Solve the problem. Round to four decimal places. -A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 44% of all employees believe their company president Possesses low ethical standards. Assume that responses were randomly and independently Collected. A president of a local company that employs 1,000 people does not believe the paperʹs Claim applies to her company. If the claim is true, how many of her companyʹs employees believe That she possesses low ethical standards?

You test 4 items from a lot of 15. What is the probability that you will test no defective items if the lot contains 3 defective items?

In a pizza takeout restaurant, the following probability distribution was obtained for the number of toppings ordered on a large pizza. Find the mean and standard deviation for the random Variable. x (x) 0 .30 1 .40 2 .20 3 .06 4 .04

Suppose the candidate pool for two appointed positions includes 6 women and 9 men. All candidates were told that the positions were randomly filled. Find the probability that two men Are selected to fill the appointed positions.

Solve the problem. Round to four decimal places. -We believe that 95% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 30 students from the Population. If the true percentage is really 95%, find the probability of observing 29 or more Students who consider statistics to be an exciting subject. Round to six decimal places.

Explain why the following is or is not a valid probability distribution for the discrete random variable x. x 10 20 30 40 50 p(x) .3 .2 .2 .2 .2

A new drug is designed to reduce a personʹs blood pressure. Thirteen randomly selected hypertensive patients receive the new drug. Suppose the probability that a hypertensive patientʹs blood pressure drops if he or she is untreated is 0.5. Then what is the probability of observing 11 or more blood pressure drops in a random sample of 13 treated patients if the new drug is in fact ineffective in reducing blood pressure? Round to six decimal places.

The number of homeruns hit during a major league baseball game follows a Poisson distribution with a mean of 3.2. Find the probability that a randomly selected game would have exactly 5 Homeruns hit.

Compute $\frac { 7 ! } { 3 ! ( 7 - 3 ) ! }$ .

Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, find each probability. a. $P ( x = 0 )$ b. $P ( x = 1 )$ C. $P ( x \leq 1 )$ d. $P ( x \geq 2 )$

Given that x is a hypergeometric random variable with N = 10, n = 3, and r = 6, compute P(x = 0).

As part of a promotion, both you and your roommate are given free cellular phones from a batch of 13 phones. Unknown to you, four of the phones are faulty and do not work. Find the probability That one of the two phones is faulty.

The Fresh Oven Bakery knows that the number of pies it can sell varies from day to day. The owner believes that on 50% of the days she sells 100 pies. On another 25% of the days she sells 150 Pies, and she sells 200 pies on the remaining 25% of the days. To make sure she has enough Product, the owner bakes 200 pies each day at a cost of $1.50 each. Assume any pies that go unsold Are thrown out at the end of the day. If she sells the pies for $3 each, find the probability Distribution for her daily profit.

The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson Distribution with a mean of 9.2. Find the probability that fewer than six tickets are written on a Randomly selected day.

The random variable x represents the number of boys in a family with three children. Assuming that births of boys and girls are equally likely, find the mean and standard deviation for the Random variable x.

An alarm company reports that the number of alarms sent to their monitoring center from customers owning their system follow a Poisson distribution with $\lambda = 4.7$ alarms per year. Identify the mean and standard deviation for this distribution.

Suppose the number of babies born each hour at a hospital follows a Poisson distribution with a mean of 3. Some people believe that the presence of a full moon increases the number of births that Take place. Suppose during the presence of a full moon, the hospital experienced eight consecutive Hours with more than four births each hour. Based on this fact, comment on the belief that the full Moon increases the number of births.