Question 1

The probability that a given computer chip will fail is 0.02.Find the probability that of 5 delivered chips,exactly 2 will fail.
A).9039
B).0922
C).0038
D).0000

Accepted Answer

The answer of The probability that a given computer chip...

Question 2

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to the nearest whole number).
A)56
B)35
C)29
D)25

Accepted Answer

The proportion of defective chips in the population is 35/(35+190) = 0.155. Therefore, the expected number of defective chips in a sample of 160 is E(X) = 0.155*160 = 24.8. Rounding to the nearest whole number gives a mean of 25.

Question 3

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?
A).0702
B).2639
C).0016
D)0

Accepted Answer

The answer of The J.O.Supplies Company buys calculators from a...

Question 4

An appliance manufacturer gives a warranty,and 95 percent of its appliances do not require repair before the warranty expires.An organization buys 10 of these appliances.Calculate an interval that contains 95.44 percent of all the appliances that will not require repair.
A)[8.12,10.88]
B)[7.43,11.57]
C)[8.81,10.19]
D)[8.55,10.45]

Accepted Answer

μ = np = 10(.95) = 9.5
σ === .6892
95.44% is a 2-standard-deviation interval: [μ ± 2σ] = [9.5 ± 2(.6892)]
= [8.12, 10.88]

Question 5

Of all individual tax returns,37 percent include errors made by the taxpayer.If IRS examiners are assigned randomly selected returns in batches of 12,find the mean and standard deviation for the number of erroneous returns per batch.
A)μ = 2.80,σ = 1.67
B)μ = 4.44,σ = 1.67
C)μ = 4.44,σ = 2.80
D)μ = 7.56,σ = 2.80

Accepted Answer

Since 37% of returns have errors, the probability of a return having an error is 0.37. We can model the number of erroneous returns per batch as a binomial distribution with n = 12 and p = 0.37. 
The mean (μ) of a binomial distribution is given by μ = np, and the standard deviation (σ) is given by σ = sqrt(np(1-p)).
Substituting n = 12 and p = 0.37, we get:
μ = 12 x 0.37 = 4.44
σ = sqrt(12 x 0.37 x 0.63) = 1.67
Therefore, the mean and standard deviation for the number of erroneous returns per batch are μ = 4.44 and σ = 1.67, respectively. 
Thus, the best choice is B.

Question 6

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 100 calculators are selected at random,what is the standard deviation of the number of defectives?
A)9.00
B)3.17
C)9.49
D)3.00

Accepted Answer

The answer of The J.O.Supplies Company buys calculators from a...

Question 7

In the most recent election,19 percent of all eligible college students voted.If a random sample of 20 students were surveyed,find the probability that none of the students voted.
A).0000
B).0014
C).0148
D).4997

Accepted Answer

The probability that one college student did not vote is 1-0.19 = 0.81. Since we are sampling 20 students, we can use the binomial distribution to calculate the probability that none of them voted: 
P(X=0) = (0.81)^20 = 0.0148
Therefore, the answer is choice C.

Question 8

In a study conducted for the state Department of Education,30 percent of the teachers who left teaching did so because they were laid off.Assume that we randomly select 10 teachers who have recently left their profession.Find the probability that exactly 4 of them were laid off.
A).3000
B).2668
C).2001
D).0090

Accepted Answer

The answer of In a study conducted for the state...

Question 9

The manager of the local grocery store has determined that,on average,4 customers use the service desk every half-hour.Assume that the number of customers using the service desk has a Poisson distribution.What is the probability that during a randomly selected half-hour period,no more than 2 customers use the service desk?
A).2381
B).1465
C).7619
D).8535
E).0916

Accepted Answer

The answer of The manager of the local grocery store...

Question 10

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 100 calculators are selected at random,what is the expected number of defectives?
A)9
B)90
C)10
D)95

Accepted Answer

The expected number of defectives can be calculated as:
Expected number of defectives = probability of defect * total number of calculators
Expected number of defectives = 0.10 * 100
Expected number of defectives = 10
Therefore, the answer is C) 10.

Question 11

In the most recent election,19 percent of all eligible college students voted.If a random sample of 20 students were surveyed,find the probability that exactly half voted in the election.
A).0000
B).0014
C).0148
D).4997

Accepted Answer

The answer of In the most recent election,19 percent of...

Question 12

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that fewer than 4 support increased spending on environmental issues.
A).0330
B).7844
C).9624
D).9954

Accepted Answer

The answer of A study conducted by a local university...

Question 13

Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours.Assume that the patient arrivals are distributed according to a Poisson distribution.Determine the probability of at least 4 but no more than 8 patients arriving in a three-hour period.
A).3813
B).5711
C).4276
D).7861
E).6174

Accepted Answer

P(4 ≤ X ≤ 8) = P(X = 8) + P(X = 7) + P(X = 6) + P(X = 5) + P(X = 4)
= (.0463) + (.0824) + (.1281) + (.1708) + (.1898) = .6174

Question 14

A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.
A).0604
B).1325
C).2552
D).8000

Accepted Answer

The probability of getting one correct answer when guessing is 1/5. Therefore, the probability of getting 4 correct answers and 26 incorrect answers is:

(30 choose 4) * (1/5)^4 * (4/5)^26 ≈ 0.1325

where (30 choose 4) represents the number of ways to choose 4 questions out of 30.

Question 15

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that exactly 3 support increased spending on environmental issues.
A).0330
B).1318
C).7844
D).9624

Accepted Answer

The scenario can be modeled using a binomial distribution with n = 6 and p = 0.25. The probability mass function for a binomial distribution is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) represents the binomial coefficient, which is computed as:

(n choose k) = n! / (k! * (n-k)!)

Using this formula, we can compute the probability of exactly 3 students out of 6 supporting increased spending on environmental issues as follows:

P(X = 3) = (6 choose 3) * 0.25^3 * 0.75^3
           = 20 * 0.015625 * 0.421875
           = 0.1318359

Rounding this to four decimal places, we get 0.1318, which corresponds to choice B.

Question 16

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that only 1 supports increased spending on environmental issues.
A).0330
B).1318
C).3560
D).7844

Accepted Answer

The answer of A study conducted by a local university...

Question 17

According to a survey of adults,64 percent have money in a regular savings account.If we were to survey 50 randomly selected adults,find the mean number of adults who would have regular savings accounts.
A)12
B)22
C)32
D)42

Accepted Answer

The answer of According to a survey of adults,64 percent...

Question 18

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 3 calculators are selected at random,what is the probability that one of the calculators will be defective?
A).0702
B).0010
C).2430
D).7290

Accepted Answer

The probability of selecting one defective calculator out of three is given by the binomial probability formula:
P(X = 1) = 3C1 * (0.1)^1 * (0.9)^2
where X is the random variable representing the number of defective calculators selected, 3C1 is the combination of choosing one defective calculator out of three, and (0.1)^1 * (0.9)^2 is the probability of selecting one defective calculator and two non-defective calculators.

Using the formula, we get:
P(X = 1) = 3 * 0.1 * 0.9^2
P(X = 1) = 0.243

Therefore, the probability that one of the calculators will be defective is 0.243 or approximately 0.24. The closest answer choice is C.

Question 19

The manager of the local grocery store has determined that,on average,4 customers use the service desk every half-hour.Assume that the number of customers using the service desk has a Poisson distribution.What is the probability that during a randomly selected half-hour period,exactly 2 customers use the service desk?
A).0183
B).0733
C).1465
D).9084
E).7619

Accepted Answer

The answer of The manager of the local grocery store...

Question 20

Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every two hours.Assume that the patient arrivals are distributed according to a Poisson distribution.Determine the probability of 6 patients arriving in a five-hour period.
A).136
B).109
C).246
D).001

Accepted Answer

P(X = 6) == .1359

Quiz 5: Discrete Random Variables

The probability that a given computer chip will fail is 0.02.Find the probability that of 5 delivered chips,exactly 2 will fail.

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to the nearest whole number) .

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

An appliance manufacturer gives a warranty,and 95 percent of its appliances do not require repair before the warranty expires.An organization buys 10 of these appliances.Calculate an interval that contains 95.44 percent of all the appliances that will not require repair.

Of all individual tax returns,37 percent include errors made by the taxpayer.If IRS examiners are assigned randomly selected returns in batches of 12,find the mean and standard deviation for the number of erroneous returns per batch.

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 100 calculators are selected at random,what is the standard deviation of the number of defectives?

In the most recent election,19 percent of all eligible college students voted.If a random sample of 20 students were surveyed,find the probability that none of the students voted.

In a study conducted for the state Department of Education,30 percent of the teachers who left teaching did so because they were laid off.Assume that we randomly select 10 teachers who have recently left their profession.Find the probability that exactly 4 of them were laid off.

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 100 calculators are selected at random,what is the expected number of defectives?

In the most recent election,19 percent of all eligible college students voted.If a random sample of 20 students were surveyed,find the probability that exactly half voted in the election.

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that fewer than 4 support increased spending on environmental issues.

A multiple-choice test has 30 questions and each one has five possible answers,of which one is correct.If all answers were guesses,find the probability of getting exactly four correct answers.

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that exactly 3 support increased spending on environmental issues.

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that only 1 supports increased spending on environmental issues.

According to a survey of adults,64 percent have money in a regular savings account.If we were to survey 50 randomly selected adults,find the mean number of adults who would have regular savings accounts.

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 3 calculators are selected at random,what is the probability that one of the calculators will be defective?

Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every two hours.Assume that the patient arrivals are distributed according to a Poisson distribution.Determine the probability of 6 patients arriving in a five-hour period.