Question 1

An archer is able to hit the bull's-eye 55% of the time. If she shoots 8 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.
A) 0.00375
B) 0.172
C) 0.0915
D) 0.263

Accepted Answer

The answer of An archer is able to hit the...

Question 2

According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.
A) 3.5
B) 2.8
C) 0.2
D) 4.0

Accepted Answer

The mean for the number of students who work full time in samples of size 16 is 22% of 16, which is 3.5.

Question 3

Focus groups of 13 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number (per group) who recognize the Yummy brand name is 10.1, and the standard deviation is 0.55. Would it be unusual to randomly select 13 people and find that fewer than 7 recognize the Yummy brand name?
A) Yes
B) No

Accepted Answer

The mean number of people who recognize the brand is 10.1 with a standard deviation of 0.55. Using the normal distribution, a value of 7 is more than 5 standard deviations below the mean (since (10.1 - 7) / 0.55 ≈ 5.64), which is considered unusual.

Question 4

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-Rolling a single "loaded" die 38 times, keeping track of the "fives" rolled.
A) Procedure results in a binomial distribution.
B) Not binomial: there are too many trials.
C) Not binomial: there are more than two outcomes for each trial.
D) Not binomial: the trials are not independent.

Accepted Answer

The procedure results in a binomial distribution because there are only two possible outcomes for each trial (five or not five), the trials are independent, and the probability of success (rolling a five) is the same for each trial.

Question 5

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than $\mu - 2 \sigma \text { or greater than } \mu + 2 \sigma$ .
-A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 504 consumers who recognize the Dull Computer
Company name?
A) Yes
B) No

Accepted Answer

The answer of Determine if the outcome is unusual. Consider...

Question 6

Find the indicated probability. Round to three decimal places.
-A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 26 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 6% rate of defects,
What is the probability that this whole shipment will be accepted?
A) 0.797
B) 0.265
C) 0.597
D) 0.135

Accepted Answer

The probability of accepting a shipment with a 6% rate of defects is 0.797.

Question 7

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than $\mu - 2 \sigma \text { or greater than } \mu + 2 \sigma$
-The Acme Candy Company claims that 8% of the jawbreakers it produces actually result in a broken jaw. Suppose 9571 persons are selected at random from those who have eaten a jawbreaker produced at Acme Candy Company. Would it be unusual for this sample of 9571 to contain 806 persons with broken jaws?
A) Yes
B) No

Accepted Answer

The answer of Determine if the outcome is unusual. Consider...

Question 8

Use the given values of n and p to find the minimum usual value $\mu - 2 \sigma \text { and the maximum usual value } \mu + 2 \sigma$ . Round
your answer to the nearest hundredth unless otherwise noted.
-$\mathrm { n } = 103 , \mathrm { p } = 0.26$

A) Minimum: 22.33; maximum: 31.23
B) Minimum: -12.85; maximum: 66.41
C) Minimum: 17.88; maximum: 35.68
D) Minimum: 35.68; maximum: 17.88

Accepted Answer

The answer of Use the given values of n and...

Question 9

If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types, we can use hypergeometric distribution. If a population has A objects of one type, while the remaining B objects are of the other type, and if n objects are sampled without replacement, then the probability of getting x objects of type $\text { A and } ( n - x )$ objects of type B is $$P ( x ) = \frac { A ! } { ( A - x ) ! x ! } \cdot \frac { B ! } { ( B - n + x ) ! ( n - x ) ! } \div \frac { ( A + B ) ! } { ( A + B - n ) ! n ! }$$ In a relatively easy lottery, a bettor selects 3 numbers from 1 to 12 (without repetition), and a winning 3-number combination is later randomly selected. What is the probability of getting all 3 winning numbers? Round your answer to four decimal places.
A) 0.0065
B) 0.0045
C) 0.0055
D) 0.0035

Accepted Answer

The answer of If we sample from a small finite...

Question 10

The probability is 0.2 that a person shopping at a certain store will spend less than $20. For groups of size 11, find the mean number who spend less than $20.
A) 4.0
B) 8.8
C) 16.0
D) 2.2

Accepted Answer

The mean number of people spending less than $20 in a group of 11 is calculated by multiplying the probability (0.2) by the group size (11), which equals 2.2.

Question 11

On a multiple choice test with 11 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.
A) 5.5
B) 2.8
C) 3.7
D) 8.3

Accepted Answer

The mean number of correct answers can be found by multiplying the probability of getting a question right (1/4) by the total number of questions (11). Thus, the mean is 11 * (1/4) = 2.75, which rounds to 2.8.

Question 12

Use the given values of n and p to find the minimum usual value $\mu - 2 \sigma \text { and the maximum usual value } \mu + 2 \sigma$ . Round
your answer to the nearest hundredth unless otherwise noted.
-$$\mathrm { n } = 336 , \mathrm { p } = 0.257 \text { Round your answers to the nearest thousandth. }$$
A) Minimum: 70.332; maximum: 102.372
B) Minimum: 78.342; maximum: 94.362
C) Minimum: 102.372; maximum: 70.332
D) Minimum: 75.024; maximum: 97.68

Accepted Answer

The answer of Use the given values of n and...

Question 13

Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 2, nothing otherwise. What is your expected value?

A) $- \$ 1.33$
B) $- \$ 3.00$
C) $\$ 5.00$
D) $\$ 3.00$

Accepted Answer

The expected value is calculated as follows: The probability of rolling a 1 or 2 is 1/3, and the payout is $5. The probability of rolling any other number is 2/3, and the payout is $0. The expected value is (1/3 * $5) + (2/3 * $0) - $3 = $1.67 - $3 = -$1.33.

Question 14

The probability of winning a certain lottery is $\frac { 1 } { 64,481 }$ . For people who play 669 times, find the standard deviation for the number of wins.
A) 1.1
B) 2.6
C) 0.3
D) 0.1

Accepted Answer

The answer of The probability of winning a certain lottery...

Question 15

Find the indicated probability. Round to three decimal places.
-The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 10 participants there have been only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer women when 10 people are picked?
A) 0.055
B) 0.044
C) 0.011
D) 0.054

Accepted Answer

The probability of getting 2 or fewer women out of 10 participants can be calculated using the binomial probability formula. With p = 0.5 for women, n = 10, and x = 0, 1, or 2, the cumulative probability is approximately 0.0547, which rounds to 0.055.

Question 16

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places.
-$\mathrm { n } = 30 , \mathrm { x } = 12 , \mathrm { p } = 0.20$

A) 0.108
B) 0.006
C) 0.014
D) 0.003

Accepted Answer

The answer of Assume that a procedure yields a binomial...

Question 17

A contractor is considering a sale that promises a profit of $25,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $2000 with a probability of 0.3. What is the expected profit?
A) $23,000
B) $16,900
C) $18,900
D) $17,500

Accepted Answer

Expected profit = (0.7 * $25,000) + (0.3 * -$2,000) = $16,900

Question 18

Find the indicated probability. Round to three decimal places.
-In a study, 38% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 12 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health.
A) 0.185
B) 0.107
C) 0.163
D) 0.270

Accepted Answer

The answer of Find the indicated probability. Round to three...

Question 19

Identify the given random variable as being discrete or continuous.
-The pH level in a shampoo
A) Continuous
B) Discrete

Accepted Answer

The pH level in a shampoo is a continuous random variable because it can take any value within a range and is measured on a continuous scale.

Question 20

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than $\mu - 2 \sigma \text { or greater than } \mu + 2 \sigma \text {. }$
-A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 522 consumers who recognize the Dull Computer
Company name?
A) Yes
B) No

Accepted Answer

The answer of Determine if the outcome is unusual. Consider...

Quiz 5: Discrete Probability Distributions

An archer is able to hit the bull's-eye 55% of the time. If she shoots 8 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Rolling a single "loaded" die 38 times, keeping track of the "fives" rolled.

Use the given values of n and p to find the minimum usual value $\mu - 2 \sigma \text { and the maximum usual value } \mu + 2 \sigma$ . Round your answer to the nearest hundredth unless otherwise noted. - $\mathrm { n } = 103 , \mathrm { p } = 0.26$

The probability is 0.2 that a person shopping at a certain store will spend less than $20. For groups of size 11, find the mean number who spend less than $20.

On a multiple choice test with 11 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.

Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 2, nothing otherwise. What is your expected value?

The probability of winning a certain lottery is $\frac { 1 } { 64,481 }$ . For people who play 669 times, find the standard deviation for the number of wins.

A contractor is considering a sale that promises a profit of $25,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $2000 with a probability of 0.3. What is the expected profit?

Identify the given random variable as being discrete or continuous. -The pH level in a shampoo

Quiz 5: Discrete Probability Distributions

An archer is able to hit the bull's-eye 55% of the time. If she shoots 8 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Rolling a single "loaded" die 38 times, keeping track of the "fives" rolled.

The probability is 0.2 that a person shopping at a certain store will spend less than $20. For groups of size 11, find the mean number who spend less than $20.

On a multiple choice test with 11 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the mean for the number of correct answers.

Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 2, nothing otherwise. What is your expected value?

The probability of winning a certain lottery is 164,481\frac { 1 } { 64,481 }64,4811​ . For people who play 669 times, find the standard deviation for the number of wins.

A contractor is considering a sale that promises a profit of $25,000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $2000 with a probability of 0.3. What is the expected profit?

Identify the given random variable as being discrete or continuous. -The pH level in a shampoo

The probability of winning a certain lottery is $\frac { 1 } { 64,481 }$ . For people who play 669 times, find the standard deviation for the number of wins.