## Essentials of Statistics Study Set 1

Statistics

## Quiz 5 :

Discrete Probability Distributions

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Q15 Q15 Q15

The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages x) in the city has the following probability distribution. The mean and the standard deviation for the number of electrical outages respectively) are

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Multiple Choice

Q52 Q52 Q52

Exhibit 5-3
Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.
-Refer to Exhibit 5-3. The expected number of new clients per month is

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Multiple Choice

Q54 Q54 Q54

Exhibit 5-3
Roth is a computer-consulting firm. The number of new clients that they have obtained each month has ranged from 0 to 6. The number of new clients has the probability distribution that is shown below.
-Refer to Exhibit 5-3. The standard deviation is

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Multiple Choice

Q61 Q61 Q61

Exhibit 5-7
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.
-Refer to Exhibit 5-7. The probability that Pete will catch fish on exactly one day is

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Multiple Choice

Q62 Q62 Q62

Exhibit 5-7
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.
-Refer to Exhibit 5-7. The probability that Pete will catch fish on one day or less is

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Multiple Choice

Q63 Q63 Q63

Exhibit 5-7
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.
-Refer to Exhibit 5-7. The expected number of days Pete will catch fish is

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Multiple Choice

Q64 Q64 Q64

Exhibit 5-7
The probability that Pete will catch fish when he goes fishing is .8. Pete is going to fish 3 days next week. Define the random variable X to be the number of days Pete catches fish.
-Refer to Exhibit 5-7. The variance of the number of days Pete will catch fish is

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Multiple Choice

Q65 Q65 Q65

Exhibit 5-8
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.
-Refer to Exhibit 5-8. The random variable x satisfies which of the following Discrete Probability Distributions?

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Multiple Choice

Q66 Q66 Q66

Exhibit 5-8
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.
-Refer to Exhibit 5-8. The appropriate probability distribution for the random variable is

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Multiple Choice

Q67 Q67 Q67

Exhibit 5-8
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.
-Refer to Exhibit 5-8. The expected value of the random variable x is

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Multiple Choice

Q68 Q68 Q68

Exhibit 5-8
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.
-Refer to Exhibit 5-8. The probability that there are 8 occurrences in ten minutes is

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Multiple Choice

Q69 Q69 Q69

Exhibit 5-8
The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3.
-Refer to Exhibit 5-8. The probability that there are less than 3 occurrences is

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Multiple Choice

Q82 Q82 Q82

Exhibit 5-13
Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below.
-Refer to Exhibit 5-13. the expected monthly production level is

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Multiple Choice

Q83 Q83 Q83

Exhibit 5-13
Oriental Reproductions, Inc. is a company that produces handmade carpets with oriental designs. The production records show that the monthly production has ranged from 1 to 5 carpets. The production levels and their respective probabilities are shown below.
-Refer to Exhibit 5-13. The standard deviation for the production is

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Multiple Choice

Q86 Q86 Q86

The demand for a product varies from month to month. Based on the past year's data, the following probability distribution shows MNM company's monthly demand.
a. Determine the expected number of units demanded per month.
b. Each unit produced costs the company $8.00, and is sold for $10.00. How much will the company gain or lose in a month if they stock the expected number of units demanded, but sell 2000 units?

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Q87 Q87 Q87

Twenty-five percent of the employees of a large company are minorities. A random sample of 7 employees is selected.
a. What is the probability that the sample contains exactly 4 minorities?
b. What is the probability that the sample contains fewer than 2 minorities?
c. What is the probability that the sample contains exactly 1 non-minority?
d. What is the expected number of minorities in the sample?
e. What is the variance of the minorities?

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Q88 Q88 Q88

A salesperson contacts eight potential customers per day. From past experience, we know that the probability of a potential customer making a purchase is .10.
a. What is the probability the salesperson will make exactly two sales in a day?
b. What is the probability the salesperson will make at least two sales in a day?
c. What percentage of days will the salesperson not make a sale?
d. What is the expected number of sales per day?

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Q89 Q89 Q89

A life insurance company has determined that each week an average of seven claims is filed in its Nashville branch.
a. What is the probability that during the next week exactly seven claims will be filed?
b. What is the probability that during the next week no claims will be filed?
c. What is the probability that during the next week fewer than four claims will be filed?
d. What is the probability that during the next week at least seventeen claims will be filed?

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Q91 Q91 Q91

Ten percent of the items produced by a machine are defective. Out of 15 items chosen at random,
a. what is the probability that exactly 3 items will be defective?
b. what is the probability that less than 3 items will be defective?
c. what is the probability that exactly 11 items will be non-defective?

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Q92 Q92 Q92

The student body of a large university consists of 30% Business majors. A random sample of 20 students is selected.
a. What is the probability that among the students in the sample at least 10 are Business majors?
b. What is the probability that at least 16 are not Business majors?
c. What is the probability that exactly 10 are Business majors?
d. What is the probability that exactly 12 are not Business majors?

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Q94 Q94 Q94

A production process produces 90% non-defective parts. A sample of 10 parts from the production process is selected.
a. What is the probability that the sample will contain 7 non-defective parts?
b. What is the probability that the sample will contain at least 4 defective parts?
c. What is the probability that the sample will contain less than 5 non-defective parts?
d. What is the probability that the sample will contain no defective parts?

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Q95 Q95 Q95

Fifty-five percent of the applications received for a particular credit card are accepted. Among the next twelve applications,
a. what is the probability that all will be rejected?
b. what is the probability that all will be accepted?
c. what is the probability that exactly 4 will be accepted?
d. what is the probability that fewer than 3 will be accepted?
e. Determine the expected number and the variance of the accepted applications.

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Q97 Q97 Q97

In a large corporation, 65% of the employees are male. A random sample of five employees is selected. Use the Binomial probability tables to answer the following questions.
a. What is the probability that the sample contains exactly three male employees?
b. What is the probability that the sample contains no male employees?
c. What is the probability that the sample contains more than three female employees?
d. What is the expected number of female employees in the sample?

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Q100 Q100 Q100

A company sells its products to wholesalers in batches of 1,000 units only. The daily demand for its product and the respective probabilities are given below.
a. Determine the expected daily demand.
b. Assume that the company sells its product at $3.75 per unit. What is the expected daily revenue?

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Q101 Q101 Q101

The records of a department store show that 20% of its customers who make a purchase return the merchandise in order to exchange it. In the next six purchases,
a. what is the probability that three customers will return the merchandise for exchange?
b. what is the probability that four customers will return the merchandise for exchange?
c. what is the probability that none of the customers will return the merchandise for exchange?

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Q102 Q102 Q102

The random variable x has the following probability distribution:
a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.
b. Calculate the expected value of x.
c. Calculate the variance of x.
d. Calculate the standard deviation of x.

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Q103 Q103 Q103

The probability function for the number of insurance policies John will sell to a customer is given by fX) = .5 - X/6) for X = 0, 1, or 2
a. Is this a valid probability function? Explain your answer.
b. What is the probability that John will sell exactly 2 policies to a customer?
c. What is the probability that John will sell at least 2 policies to a customer?
d. What is the expected number of policies John will sell?
e. What is the variance of the number of policies John will sell?

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Q105 Q105 Q105

In a large university, 75% of students live in dormitories. A random sample of 5 students is selected. Use the binomial probability tables to answer the following questions.
a. What is the probability that the sample contains exactly three students who live in the dormitories?
b. What is the probability that the sample contains no students who lives in the dormitories?
c. What is the probability that the sample contains more than three students who do not live in the dormitories?
d. What is the expected number of students in the sample) who do not live in the dormitories?

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Q106 Q106 Q106

A manufacturing company has 5 identical machines that produce nails. The probability that a machine will break down on any given day is .1. Define a random variable X to be the number of machines that will break down in a day.
a. What is the appropriate probability distribution for X? Explain how X satisfies the properties of the distribution.
b. Compute the probability that 4 machines will break down.
c. Compute the probability that at least 4 machines will break down.
d. What is the expected number of machines that will break down in a day?
e. What is the variance of the number of machines that will break down in a day?

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Q107 Q107 Q107

On the average, 6.7 cars arrive at the drive-up window of a bank every hour. Define the random variable X to be the number of cars arriving in any hour.
a. What is the appropriate probability distribution for X? Explain how X satisfies the properties of the distribution.
b. Compute the probability that exactly 5 cars will arrive in the next hour.
c. Compute the probability that no more than 5 cars will arrive in the next hour.

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Q108 Q108 Q108

Twenty-five percent of all resumes received by a corporation for a management position are from females. Fifteen resumes will be received tomorrow.
a. What is the probability that exactly 5 of the resumes will be from females?
b. What is the probability that fewer than 3 of the resumes will be from females?
c. What is the expected number of resumes from women?
d. What is the variance of the number of resumes from women?

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Q109 Q109 Q109

The average number of calls received by a switchboard in a 30-minute period is 15.
a. What is the probability that between 10:00 and 10:30 the switchboard will receive exactly 10 calls?
b. What is the probability that between 10:00 and 10:30 the switchboard will receive more than 9 calls but fewer than 15 calls?
c. What is the probability that between 10:00 and 10:30 the switchboard will receive fewer than 7 calls?

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Q110 Q110 Q110

Two percent of the parts produced by a machine are defective. Twenty parts are selected at random. Use the binomial probability tables to answer the following questions.
a. What is the probability that exactly 3 parts will be defective?
b. What is the probability that the number of defective parts will be more than 2 but fewer than 6?
c. What is the probability that fewer than 4 parts will be defective?
d. What is the expected number of defective parts?
e. What is the variance for the number of defective parts?

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Q112 Q112 Q112

Seven students have applied for merit scholarships. This year 3 merit scholarships were awarded. If a random sample of 3 applications from the population of 7) is selected,
a. what is the probability that 2 students were recipients of scholarships?
b. what is the probability that no students were the recipients of scholarship?

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Q114 Q114 Q114

Twenty percent of the applications received for a particular position are rejected. What is the probability that among the next fourteen applications,
a. none will be rejected?
b. all will be rejected?
c. less than 2 will be rejected?
d. more than four will be rejected?
e. Determine the expected number of rejected applications and its variance.

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Q115 Q115 Q115

An insurance company has determined that each week an average of nine claims are filed in their Atlanta branch.
What is the probability that during the next week
a. exactly seven claims will be filed?
b. no claims will be filed?
c. less than four claims will be filed?
d. at least eighteen claims will be filed?

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Q116 Q116 Q116

A local university reports that 10% of their students take their general education courses on a pass/fail basis. Assume that fifteen students are registered for a general education course.
a. What is the expected number of students who have registered on a pass/fail basis?
b. What is the probability that exactly five are registered on a pass/fail basis?
c. What is the probability that more than four are registered on a pass/fail basis?
d. What is the probability that less than two are registered on a pass/fail basis?

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Q117 Q117 Q117

A production process produces 2% defective parts. A sample of 5 parts from the production is selected. What is the probability that the sample contains exactly two defective parts? Use the binomial probability function and show your computations to answer this question.

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Short Answer

Q118 Q118 Q118

A retailer of electronic equipment received six VCRs from the manufacturer. Three of the VCRs were damaged in the shipment. The retailer sold two VCRs to two customers.
a. Can a binomial formula be used for the solution of the above problem?
b. What kind of probability distribution does the above satisfy, and is there a function for solving such problems?
c. What is the probability that both customers received damaged VCRs?
d. What is the probability that one of the two customers received a defective VCR?

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Q120 Q120 Q120

The number of bad checks received per day by a store and the respective probabilities are shown below.
a. What is the expected number of bad checks received per day?
b. Determine the variance in the number of bad checks received per day.
c. What is the standard deviation?

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Q121 Q121 Q121

The following table shows part of the probability distribution for a random variable x.
x fx)
0 0.2
1 ?
2 0.15
3 ?
4 0.15
a. The mean of the above distribution is known to be 1.8 i.e., Ex) = 1.8). Determine f1) and f3).
b. Compute the variance and the standard deviation for the above probability distribution.

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