Question 1

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that all three faculty selected are men is approximately _______
A)0.05
B)0.33
C)0.11
D)0.80
E)0.90

Accepted Answer

The answer of Suppose an interdisciplinary committee of 3 faculty...

Question 2

Circuit boards for wireless telephones are etched,in an acid bath,in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A particular batch contains two defective boards; and x is the number of defective boards in the sample.P(x=0)is _______.
A)0.1315
B)0.8642
C)0.0042
D)0.6134
E)0.8134

Accepted Answer

The probability of selecting 0 defective boards out of 7 when there are 2 defective boards in a batch of 100 is calculated using the hypergeometric distribution formula. The probability is P(x=0) = [(98 choose 7) / (100 choose 7)], which equals approximately 0.8642.

Question 3

The probability of selecting 3 female employees and 7 male employees to win a promotional trip a company with 10 female and 50 male employees would best be modeled with the _______.
A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Accepted Answer

The hypergeometric distribution is the best choice for this scenario as we are selecting a specific number of individuals from a sample without replacement, and the probability of success (selecting a female employee) changes each time we make a selection due to the reduced population size.

Question 4

The Poisson distribution is being used to approximate a binomial distribution.If n=60 and p=0.02,what value of lambda would be used?
A)0.02
B)12
C)0.12
D)1.2
E)120

Accepted Answer

When n (the sample size) is large and p (the probability of success in each trial) is small, the binomial distribution can be approximated by the Poisson distribution with λ=np.

In this case, n=60 and p=0.02, so np=60*0.02=1.2. Therefore, the value of λ that would be used to approximate the binomial distribution would be 1.2. Thus, the answer is D) 1.2.

Question 5

Aluminum castings are processed in lots of five each.A sample of two castings is randomly selected from each lot for inspection.A particular lot contains one defective casting; and x is the number of defective castings in the sample.P(x=0)is _______.
A)0.2
B)0.4
C)0.6
D)0.8
E)1.0

Accepted Answer

The answer of Aluminum castings are processed in lots of...

Question 6

The number of bags arriving on the baggage claim conveyor belt in a 3 minute time period would best be modeled with the _________.
A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Accepted Answer

The Poisson distribution is appropriate for modeling the number of events occurring in a fixed interval of time or space, under certain assumptions including that events occur independently and at a constant average rate. This seems to fit the scenario of bags arriving on a baggage claim conveyor belt during a fixed time period.

Question 7

Which of the following conditions is not a condition for the hypergeometric distribution?
A)the probability of success is the same on each trial
B)sampling is done without replacement
C)there are only two possible outcomes
D)trials are dependent
E)n < 5%N

Accepted Answer

The answer of Which of the following conditions is not...

Question 8

Circuit boards for wireless telephones are etched,in an acid bath,in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A particular batch contains two defective boards; and x is the number of defective boards in the sample.P(x=2)is _______.
A)0.1315
B)0.8642
C)0.0042
D)0.6134
E)0.0034

Accepted Answer

This is a binomial distribution problem with n=7 (sample size) and p=0.02 (proportion of defective boards in the batch). We want to find P(x=2), which is the probability of getting exactly two defective boards in the sample of 7. Using the binomial probability formula, we get:

P(x=2) = (7 choose 2) * (0.02)^2 * (0.98)^5 = 0.0042

Therefore, the answer is choice C.

Question 9

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that one male faculty and two female faculty are selected is approximately ______
A)0.15
B)0.06
C)0.33
D)0.48
E)0.58

Accepted Answer

The answer of Suppose an interdisciplinary committee of 3 faculty...

Question 10

If sampling is performed without replacement,the hypergeometric distribution should be used.However,the binomial may be used to approximate this if _______.
A)n > 5%N
B)n < 5%N
C)the population size is very small
D)there are more than two possible outcomes of each trial
E)the outcomes are continuous

Accepted Answer

When the sample size is less than 5% of the population size, the difference between sampling with or without replacement is negligible and the binomial distribution can be used to approximate the hypergeometric distribution.

Question 11

Ten policyholders file claims with CareFree Insurance.Three of these claims are fraudulent.Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,P(x=1)is _______________.
A)0.5250
B)0.4410
C)0.3000
D)0.6957
E)0.9957

Accepted Answer

The probability of selecting exactly 1 fraudulent claim out of 3 chosen from 10, where 3 are fraudulent and 7 are legitimate, can be calculated using combinations. The probability is found by dividing the number of ways to choose 1 fraudulent and 2 legitimate claims by the total ways to choose any 3 claims from 10. This is calculated as: $\frac{{\binom{3}{1} \times \binom{7}{2}}}{{\binom{10}{3}}} = \frac{{3 \times 21}}{{120}} = 0.525$.

Question 12

The number of defects per 1,000 feet of extruded plastic pipe is best modeled with the ________________.
A)Poisson distribution
B)Pascal distribution
C)binomial distribution
D)hypergeometric distribution
E)exponential distribution

Accepted Answer

The Poisson distribution is commonly used to model the number of defects per unit length in manufacturing processes. It is appropriate when defects occur randomly and independently of one another, which is likely to be the case with a continuous process like extruding plastic pipe. The other distributions listed are not typically used to model defect rates in this context.

Question 13

The probability of selecting 2 baseball players and 3 basketball players for an intermural competition at a small sports camp would best be modeled with the _______.
A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Accepted Answer

The problem involves selecting a specific number of players (2 baseball and 3 basketball) from a larger group (all players at the camp). This is a classic example of a hypergeometric distribution.

Question 14

On Monday mornings,customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen minute interval.Using the Poisson distribution,the probability that five cars will arrive during the next five minute interval is _____________.
A)0.1008
B)0.0361
C)0.1339
D)0.1606
E)0.3610

Accepted Answer

We need to find the probability that 5 cars will arrive in the next 5-minute interval.

First, we need to convert the arrival rate from a 15-minute interval to a 5-minute interval.

Arrival rate in a 5-minute interval = (Arrival rate in a 15-minute interval) / 3

Arrival rate in a 5-minute interval = 6 / 3 = 2

Now we can use the Poisson distribution formula:

P(X = 5) = (e^(-λ) * λ^x) / x!

Where: 
λ = Arrival rate in the interval = 2 
x = Number of arrivals we're interested in = 5

P(X = 5) = (e^(-2) * 2^5) / 5!

P(X = 5) = 0.0361

Therefore, the answer is B) 0.0361.

Question 15

One hundred policyholders file claims with CareFree Insurance.Ten of these claims are fraudulent.Claims manager Earl Evans randomly selects four of the one hundred claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,x has a _______________ distribution.
A)continuous
B)normal
C)binomial
D)hypergeometric
E)exponential

Accepted Answer

The situation describes a hypergeometric distribution because it involves selecting a sample without replacement from a finite population that contains exactly two types of objects (fraudulent and non-fraudulent claims), which fits the definition of a hypergeometric distribution.

Question 16

Ten policyholders file claims with CareFree Insurance.Three of these claims are fraudulent.Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,P(x=0)is _______________.
A)0.0083
B)0.3430
C)0.0000
D)0.2917
E)0.8917

Accepted Answer

The probability of selecting 0 fraudulent claims out of 3 when there are 3 fraudulent claims and 7 legitimate claims in total can be calculated using combinations. The total number of ways to select 3 claims out of 10 is 10C3 = 120. The number of ways to select 0 fraudulent claims (thus, all 3 are legitimate) is 7C3 = 35. Therefore, P(x=0) = 35/120 = 0.2917.

Question 17

Circuit boards for wireless telephones are etched,in an acid bath,in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A batch contains two defective boards; and x is the number of defective boards in the sample.P(x=1)is _______.
A)0.1315
B)0.8642
C)0.0042
D)0.6134
E)0.6789

Accepted Answer

The probability P(x=1) can be calculated using the hypergeometric distribution formula, which is appropriate for sampling without replacement from a finite population. The formula for finding the probability of getting exactly k successes (defective boards in this case) in n draws (sample size) from a population of N containing K successes (defective boards in the batch) is:$$ P(x=k) = \frac{{\binom{K}{k} \cdot \binom{N-K}{n-k}}}{{\binom{N}{n}}} $$Given values are N=100 (total boards), K=2 (defective boards), n=7 (sample size), and k=1 (number of defective boards in the sample). Plugging these values into the formula gives:$$ P(x=1) = \frac{{\binom{2}{1} \cdot \binom{98}{6}}}{{\binom{100}{7}}} $$$$ P(x=1) = \frac{{2 \cdot 1221759}}{{16007560800}} \approx 0.1315 $$Therefore, the correct answer is A) 0.1315, which represents the probability of finding exactly one defective board in the sample.

Question 18

The Poisson distribution is being used to approximate a binomial distribution.If n=30 and p=0.03,what value of lambda would be used?
A)0.09
B)9.0
C)0.90
D)90
E)30

Accepted Answer

The answer of The Poisson distribution is being used to...

Question 19

Aluminum castings are processed in lots of five each.A sample of two castings is randomly selected from each lot for inspection.A particular lot contains one defective casting; and x is the number of defective castings in the sample.P(x=1)is _______.
A)0.2
B)0.4
C)0.6
D)0.8
E)1.0

Accepted Answer

Since there is only one defective casting in the lot, the probability of selecting a defective casting in the first draw is 1/5. Therefore, the probability of selecting a non-defective casting in the first draw is 4/5. For the second draw, there are only four castings left in the lot, one of which is defective. Therefore, the probability of selecting the defective casting in the second draw given that a non-defective casting was selected in the first draw is 1/4. Conversely, the probability of selecting a non-defective casting in the second draw given that a non-defective casting was selected in the first draw is 3/4. Thus, the probability of selecting one defective casting in the sample is the product of the probabilities of selecting a non-defective casting in the first draw and a defective casting in the second draw, or (4/5) × (1/4) = 1/5 = 0.2. Therefore, P(x=1) = 0.2.

Question 20

The hypergeometric distribution must be used instead of the binomial distribution when ______
A)sampling is done with replacement
B)sampling is done without replacement
C)n≥5% N
D)both b and c
E)there are more than two possible outcomes

Accepted Answer

The answer of The hypergeometric distribution must be used instead...

Quiz 5: Discrete Distributions

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that all three faculty selected are men is approximately _______

Circuit boards for wireless telephones are etched,in an acid bath,in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A particular batch contains two defective boards; and x is the number of defective boards in the sample.P(x=0) is _______.

The probability of selecting 3 female employees and 7 male employees to win a promotional trip a company with 10 female and 50 male employees would best be modeled with the _______.

The Poisson distribution is being used to approximate a binomial distribution.If n=60 and p=0.02,what value of lambda would be used?

Aluminum castings are processed in lots of five each.A sample of two castings is randomly selected from each lot for inspection.A particular lot contains one defective casting; and x is the number of defective castings in the sample.P(x=0) is _______.

The number of bags arriving on the baggage claim conveyor belt in a 3 minute time period would best be modeled with the _________.

Which of the following conditions is not a condition for the hypergeometric distribution?

Circuit boards for wireless telephones are etched,in an acid bath,in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A particular batch contains two defective boards; and x is the number of defective boards in the sample.P(x=2) is _______.

Suppose an interdisciplinary committee of 3 faculty members is to be selected from a group consisting of 4 men and 5 women.The probability that one male faculty and two female faculty are selected is approximately ______

If sampling is performed without replacement,the hypergeometric distribution should be used.However,the binomial may be used to approximate this if _______.

Ten policyholders file claims with CareFree Insurance.Three of these claims are fraudulent.Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,P(x=1) is _______________.

The number of defects per 1,000 feet of extruded plastic pipe is best modeled with the ________________.

The probability of selecting 2 baseball players and 3 basketball players for an intermural competition at a small sports camp would best be modeled with the _______.

On Monday mornings,customers arrive at the coffee shop drive thru at the rate of 6 cars per fifteen minute interval.Using the Poisson distribution,the probability that five cars will arrive during the next five minute interval is _____________.

One hundred policyholders file claims with CareFree Insurance.Ten of these claims are fraudulent.Claims manager Earl Evans randomly selects four of the one hundred claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,x has a _______________ distribution.

Ten policyholders file claims with CareFree Insurance.Three of these claims are fraudulent.Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample,P(x=0) is _______________.

Circuit boards for wireless telephones are etched,in an acid bath,in batches of 100 boards.A sample of seven boards is randomly selected from each lot for inspection.A batch contains two defective boards; and x is the number of defective boards in the sample.P(x=1) is _______.

The Poisson distribution is being used to approximate a binomial distribution.If n=30 and p=0.03,what value of lambda would be used?

Aluminum castings are processed in lots of five each.A sample of two castings is randomly selected from each lot for inspection.A particular lot contains one defective casting; and x is the number of defective castings in the sample.P(x=1) is _______.

The hypergeometric distribution must be used instead of the binomial distribution when ______