Exam 4: Discrete Random Variables

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 30% of all employees believe their company president Possesses low ethical standards. Suppose 20 of a companyʹs employees are randomly and Independently sampled. Assuming the paperʹs claim is correct, find the probability that more than Eight but fewer than 12 of the 20 sampled believe the companyʹs president possesses low ethical Standards. Round to six decimal places.

The probability that an individual is left-handed is 0.12. In a class of 10 students, what is the mean and standard deviation of the number of left-handed students? Round to the nearest hundredth When necessary.

Classify the following random variable according to whether it is discrete or continuous. The temperature in degrees Fahrenheit on July 4th in Juneau, Alaska

Compute $\left( \begin{array} { l } 4 \\ 4 \end{array} \right)$

Given that x is a hypergeometric random variable with N = 10, n = 3, and r = 5: a. Display the probability distribution in tabular form. b. Compute $\mu$ and $\sigma$ for $x$ . c. What is the probability that $x$ will fall within the interval $\mu \pm 2 \sigma$

Given that x is a hypergeometric random variable with N = 8, n = 4, and r = 3: a. Display the probability distribution in tabular form. $\text { b. Find } P ( x \leq 2 ) \text {. }$

Solve the problem. Round to four decimal places. -A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters were randomly selected from the population of all eligible voters. Use a Binomial probability table to find the probability that more than 12 of the eligible voters sampled Will vote in the next presidential election.

Given that x is a hypergeometric random variable with N = 8, n = 4, and r = 3, compute the variance of x.

Consider the given discrete probability distribution. Construct a graph for p(x). x 1 2 3 4 5 6 p(x) .30 .25 .20 .15 .05 .05

A small life insurance company has determined that on the average it receives 4 death claims per day. Find the probability that the company receives at least seven death claims on a randomly selected day.

Consider the given discrete probability distribution. Find $P ( x > 3 )$ .

The binomial distribution can be used to model the number of rare events that occur over a given time period.

50 students were randomly sampled and asked questions about their exercise habits. One of the questions they were asked concerned the frequency of exercise, defined to be the number of times They exercised in a week. This variable would be characterized as which type of random variable?

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 probability That none of the four cans selected contains an incorrect mix of paint.

Consider the given discrete probability distribution. x 1 2 3 4 5 p(x) .1 .2 .2 .3 .2 a. Find $\mu = E ( x )$ . b. Find $\sigma = \sqrt { E \left[ ( x - \mu ) ^ { 2 } \right] }$ . c. Find the probability that the value of $x$ falls within one standard deviation of the mean. Compare this result to the Empirical Rule.

An automobile manufacturer has determined that 30% of all gas tanks that were installed on its 2002 compact model are defective. If 9 of these cars are independently sampled, what is the probability that more than half need new gas tanks?

Suppose that 4 out of 12 liver transplants done at a hospital will fail within a year. Consider a random sample of 3 of these 12 patients. What is the probability that all 3 patients will result in Failed transplants?

Explain why the following is or is not a valid probability distribution for the discrete random variable x. x 0 2 4 6 8 p(x) -.1 .1 .2 .3 .5

For a binomial distribution, which probability is not equal to the probability of 1 success in 5 trials where the probability of success is .4?