# Experiments, Random Variables, and Distributions

10. The following examples are experiments and their associated random variables. In each case identify the values the random variable can assume and state whether the random variable is discrete or continuous.

a. Take a 20-question exam

Number of questions answered correctly

b. Observe cars arriving at a tollbooth for I hour

Number of cars arriving at the tollbooth

c. Audit SO tax returns

Number of returns containing errors

d. Observe an employee's work for 8 hours

Number of nonproductive hours

e. Weigh a shipment of goods

Number of pounds

11. Suppose a manager must choose between the following two mathematical models of a given situation: (a) a relatively simple model that is a reasonable approximation of the real situation and (b) a thorough and complex model that is the most accurate mathematical representation of the real situation. Why might the model described in (a) be preferred by the manager?

12. A sample of 100 customers of Washington Gas resulted in the following frequency distribution of monthly charges:

Amount Number

0-49 13

50-99 22

100-149 34

150-199 26

200-249 5

a Let A be the event that monthly charges are $150 or more. Find P(A).

b. Let B be the event that monthly charges are less than $150. Find P(B).

13. Suppose that a sample space has five equally likely experimental outcomes: E1, B2, E3, E4, and E5. Let

A = {E1, E2}

B = {E3, E$}

C = {E, E3, E5}

a. Find P(A), P(B). and P(C)

b. P(A U B). Are A and B mutually exclusive?

c. Find Ac. Ct

d. EindAUBCandP(AUBC)

e. Find P(B U C)

https://brainmass.com/statistics/probability/experiments-random-variables-and-distributions-121687

#### Solution Preview

Probability

10. The following examples are experiments and their associated random variables. In each case identify the values the random variable can assume and state whether the random variable is discrete or continuous.

a. Take a 20-question exam

Number of questions answered correctly

Possible values: 0, 1, 2, ... , 19, 20

discrete

b. Observe cars arriving at a tollbooth for 1 hour

Number of cars arriving at the tollbooth

Possible values: 0, 1, 2, ... up to the maximum (for example, if the tollbooth can handle 1 car per minute, the maximum number of cars is 60)

discrete

c. Audit SO tax returns

Number of returns containing errors

Possible values: 0, 1, 2, ... up to the number of returns you audit

discrete

d. Observe an ...

#### Solution Summary

This problem set has four questions involving random variables, mathematical models, probabilities of events, and probability rules (union, intersection, complement).

Describe a discrete random variable, a Bernoulli experiment

Part A: A random variable is a numerical value determined by the outcome of an experiment. Briefly describe a discrete random variable. For each of the following indicate whether the random variable is discrete, and provide your reasoning.

i) The distance between Gainesville, Florida, and all Florida cities with population at least 50,000

ii) The number of hits for a team in a high school girls' softball game

iii) The length of time to get a haircut.

iv) The number of cars a jogger passes each morning while running.

Part B:

(a) Describe a Bernoulli experiment and give two examples.

(b) What is the connection between a Bernoulli experiment and a binomial distribution? Explain.

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