Question 1

On Saturdays, cars arrive at Sam Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen-minute interval.Using the Poisson distribution, the probability that five cars will arrive during the next fifteen-minute interval is ___.
A)0.1008
B)0.0361
C)0.1339
D)0.1606
E)0.5000

Accepted Answer

The answer of On Saturdays, cars arrive at Sam Schmitt's...

Question 2

For the Poisson distribution of a random variable lambda (λ)is 5 occurrences per ten-minute time interval.If we want to analyze the number of occurrences per hour, we must use an adjusted value for lambda equal to ___.
A)5
B)60
C)30
D)10
E)20

Accepted Answer

To adjust for the number of occurrences per hour, we need to multiply lambda by the number of ten-minute intervals in an hour, which is 6 (60 minutes divided by 10-minute intervals). Therefore, the adjusted value for lambda is λ' = 5 x 6 = 30. So the best choice is C.

Question 3

On Saturdays, cars arrive at Sami Schmitt's Scrub and Shine Car Wash 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

To use the Poisson distribution, we need to know the average rate of cars arriving, which can be calculated by converting the given rate of 6 cars per 15 minutes to a rate per 5 minutes:

6 cars / 15 minutes = 0.4 cars per minute
0.4 cars per minute * 5 minutes = 2 cars in 5 minutes

So the average rate of cars arriving is 2 cars in a 5 minute interval. Now we can use the Poisson distribution formula to calculate the probability of 5 cars arriving:

P(X = 5) = (e^(-2) * 2^5) / 5!
P(X = 5) = 0.0361

Therefore, the probability that five cars will arrive during the next five minute interval is 0.0361. The best choice is (B).

Question 4

The number of phone calls arriving at a switchboard in a 10 minute time period would best be modelled with the ___.
A)binomial distribution
B)hypergeometric distribution
C)Poisson distribution
D)hyperbinomial distribution
E)exponential distribution

Accepted Answer

The Poisson distribution is best used to model the number of arrivals of a certain event in a given time period, when the arrivals are random and independent, and the average rate of arrivals is known. In this case, the number of phone calls arriving at a switchboard in a 10 minute time period would fit these criteria, making the Poisson distribution the best choice for modelling.

Question 5

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x>0)is ___.
A)0.2172
B)0.9533
C)0.1846
D)0.9222
E)1.0000

Accepted Answer

The answer of Dorothy Little purchased a mailing list of...

Question 6

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x<2)is ___.
A)0.3370
B)0.9853
C)0.9785
D)0.2333
E)0.5000

Accepted Answer

The answer of Dorothy Little purchased a mailing list of...

Question 7

If x is a binomial random variable with n=8 and p=0.6, the mean value of x is ___.
A)6
B)4.8
C)3.2
D)8
E)48

Accepted Answer

The mean value of a binomial random variable with n trials and probability of success p is given by np. Thus, np = 8(0.6) = 4.8. Therefore, the answer is B.

Question 8

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2013.A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contains errors, the mean value of x is ___.
A)400
B)2
C)200
D)5
E)1

Accepted Answer

The mean value of x, the number of vouchers with errors in the sample, is calculated as the sample size (10) multiplied by the probability of error (0.20), which equals 2.

Question 9

If x is a binomial random variable with n=8 and p=0.6, what is the probability that x is equal to 4?
A)0.500
B)0.005
C)0.124
D)0.232
E)0.578

Accepted Answer

The probability of a binomial random variable x being equal to k is given by the formula P(x=k) = C(n, k) * p^k * (1-p)^(n-k). For n=8, k=4, and p=0.6, this calculates to approximately 0.232.

Question 10

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 3 cars arriving over a five-minute interval is ___.
A)0.2700
B)0.0498
C)0.2240
D)0.0001
E)0.0020

Accepted Answer

The Poisson distribution formula is P(X=k) = e^(-λ) * λ^k / k!, where λ is the mean and k is the number of events. In this case, λ=3 and k=3, so we plug in those values to get P(X=3) = e^(-3) * 3^3 / 3! = 0.2240. Therefore, the answer is C.

Question 11

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

In Poisson approximation to binomial, lambda=np. 
Therefore, lambda=60*0.02=1.2. For a Poisson distribution to approximate a binomial distribution, the mean of the Poisson distribution (lambda) should be equal to the product of n and p, which is 60*0.02=1.2. Therefore, the value of lambda that would be used is 1.2, which is answer choice D.

Question 12

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2013.A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contain errors, P(x = 0)is ___.
A)0.8171
B)0.1074
C)0.8926
D)0.3020
E)0.2000

Accepted Answer

This is a binomial distribution problem, where n = 10 (sample size), p = 0.2 (probability of error in the population), and x = number of vouchers with errors in the sample.

P(x = 0) = (10 choose 0) * 0.2^0 * 0.8^10 = 0.1074 (using binomial probability formula)

Therefore, the answer is Choice B.

Question 13

The Poisson distribution is being used to approximate a binomial distribution.If n=40 and p=0.06, what value of lambda would be used?
A)0.06
B)2.4
C)0.24
D)24
E)40

Accepted Answer

For a Poisson distribution to approximate a binomial distribution, the lambda parameter should be equal to np. Therefore, lambda = np = (40)(0.06) = 2.4, which is choice B.

Question 14

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2013.A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contains errors, the standard deviation of x is ___.
A)1.26
B)1.60
C)14.14
D)3.16
E)0.00

Accepted Answer

The standard deviation of a sample proportion can be calculated using the formula for the standard deviation of a hypergeometric distribution: sqrt[n * (p) * (1-p) * ((N-n)/(N-1))], where n is the sample size, p is the proportion of errors, and N is the population size. Plugging in the values: sqrt[10 * 0.2 * 0.8 * ((2000-10)/(2000-1))] ≈ 1.26.

Question 15

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x=0)is ___.
A)0.8154
B)0.0467
C)0.0778
D)0.4000
E)0.5000

Accepted Answer

The answer of Dorothy Little purchased a mailing list of...

Question 16

If x is a binomial random variable with n=8 and p=0.6, the standard deviation of x is ___.
A)4.8
B)3.2
C)1.92
D)1.39
E)1.00

Accepted Answer

The standard deviation of a binomial distribution is calculated using the formula √(n*p*(1-p)). For n=8 and p=0.6, it is √(8*0.6*0.4) = √1.92 ≈ 1.39.

Question 17

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 5 cars arriving over a five-minute interval is ___.
A)0.0940
B)0.0417
C)0.1500
D)0.1008
E)0.2890

Accepted Answer

The answer of The number of cars arriving at a...

Question 18

Dorothy Little purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list she doubts the authenticity of the list.She randomly selects five names from the list for validation.If 40% of the names on the list are non-authentic, and x is the number on non-authentic names in her sample, the expected (average)value of x is ___.
A)2.50
B)2.00
C)1.50
D)1.25
E)1.35

Accepted Answer

The answer of Dorothy Little purchased a mailing list of...

Question 19

The number of defects per 1,000 feet of extruded plastic pipe is best modelled 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 rare events occurring in a fixed interval of time or space. Since defects in extruded plastic pipes are typically rare events, the Poisson distribution is the best choice for modeling the number of defects per 1,000 feet of pipe.

Question 20

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2013.A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers.Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x.If 20% of the population of vouchers contain errors, P(x>0)is ___.
A)0.8171
B)0.1074
C)0.8926
D)0.3020
E)1.0000

Accepted Answer

Since 20% of the population of vouchers contain errors, the sample follows a binomial distribution with n = 10 and p = 0.2. 
P(x > 0) = 1 - P(x = 0) 
= 1 - (0.8)^10 
= 1 - 0.1074 
= 0.8926 
Therefore, the answer is C.

Quiz 5: Discrete Distributions

On Saturdays, cars arrive at Sam Schmitt's Scrub and Shine Car Wash at the rate of 6 cars per fifteen-minute interval.Using the Poisson distribution, the probability that five cars will arrive during the next fifteen-minute interval is ___.

For the Poisson distribution of a random variable lambda (λ) is 5 occurrences per ten-minute time interval.If we want to analyze the number of occurrences per hour, we must use an adjusted value for lambda equal to ___.

On Saturdays, cars arrive at Sami Schmitt's Scrub and Shine Car Wash 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 ___.

The number of phone calls arriving at a switchboard in a 10 minute time period would best be modelled with the ___.

If x is a binomial random variable with n=8 and p=0.6, the mean value of x is ___.

If x is a binomial random variable with n=8 and p=0.6, what is the probability that x is equal to 4?

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 3 cars arriving over a five-minute interval is ___.

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?

The Poisson distribution is being used to approximate a binomial distribution.If n=40 and p=0.06, what value of lambda would be used?

If x is a binomial random variable with n=8 and p=0.6, the standard deviation of x is ___.

The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals.The probability of 5 cars arriving over a five-minute interval is ___.

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