Question 1

A company manufactures batteries in batches of 6 and there is a 3% rate of defects. Find the mean number of defects per batch.

Accepted Answer

A)  5.8 defects 
B)  1.8 defects 
C)  0.2 defects 
D)  18 defects

Question 2

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 9 times, keeping track of the occurrences of a winning number of
"16)"

Accepted Answer

A)  Not binomial: the trials are not independent. 
B)  The procedure results in a binomial distribution.. 
C)  Not binomial: there are more than two outcomes for each trial. 
D)  Not binomial: there are too many trials.

Question 3

In a magazine survey, 427 women are randomly selected without replacement and each woman is asked what she purchases online. Responses consist of whether clothing was
identified. Determine whether the given procedure results in a distribution that is either
binomial or can be treated as binomial. If not binomial, identify at least one requirement that
is not satisfied.

Accepted Answer

The answer of In a magazine survey, 427 women are...

Question 4

In a certain town, 22% of voters favor a given ballot measure. For groups of 21 voters, find the variance for the number who favor the measure.

Accepted Answer

A)  $3.6$ voters $^ { 2 }$ 
B)  $4.6$ voters $^ { 2 }$ 
C)  $1.9$ voters $^ { 2 }$ 
D)  13 voters $^ { 2 }$

Question 5

A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in? Assume that each serve is independent of the others.

Accepted Answer

A)  0.154 
B)  0.00184 
C)  0.133 
D)  0.0635

Question 6

Do probability distributions measure what did happen or what will probably happen? How do we use probability distributions to make decisions?

Accepted Answer

The answer of Do probability distributions measure what did happen...

Question 7

Find the mean, $\mu$ for the binomial distribution which has the stated values of  n and p. Round answer to the nearest tenth.  n=676 ; p=0.7

Accepted Answer

A)  $\mu = 474.9$ 
B)  $\mu = 473.2$ 
C)  $\mu = 474.5$ 
D)  $\mu = 471.7$

Question 8

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

Accepted Answer

A)  1.5 twos 
B)  3 twos 
C)  7.5 twos 
D)  2.25 twos

Question 9

Sampling without replacement involves dependent events, so this would not be considered a binomial experiment. Explain the circumstances under which sampling
without replacement could be considered independent and, thus, binomial.

Accepted Answer

The answer of Sampling without replacement involves dependent events, so...

Question 10

The probability that a call received by a certain switchboard will be a wrong number is 0.02. Use the Poisson distribution to approximate the probability that among 150 calls received by the switchboard, there are at least two wrong numbers. Round your answer to four
Decimal places.

Accepted Answer

A)  0.8009 
B)  0.7760 
C)  0.2240 
D)  0.1991 
E)  0.5768

Question 11

Find the standard deviation, $\sigma$ , for the binomial distribution which has  n=48  and $p = 3 / 5$ Round your answer to the nearest hundredth.

Accepted Answer

A)  $\sigma = 6.66$ 
B)  $\sigma = 0.98$ 
C)  $\sigma = 7.51$ 
D)  $\sigma = 3.39$

Question 12

Identify the given random variable as being discrete or continuous. The cost of a randomly selected orange.

Accepted Answer

A)  Discrete 
B)  Continuous

Question 13

A game is said to be "fair" if the expected value for winnings is 0, that is, in the long run, the player can expect to win 0. Consider the following game. The game costs $1 to play and the winnings are $5 for red, $3 for blue, $2 for yellow, and nothing for white. The following probabilities apply. What are your expected winnings? Does the game favor the player or the owner? 
$\begin{array} { r | c } 
\text { Outcome } & \text { Probability } \
\hline \text { Red } & .02 \
\text { Blue } & .04 \
\text { Yellow } & .16 \
\text { White } & .78
\end{array}$

Accepted Answer

The answer of A game is said to be "fair"...

Question 14

On a multiple choice test with 17 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.

Accepted Answer

A)  8.5 questions 
B)  12.8 questions 
C)  4.3 questions 
D)  5.7 questions

Question 15

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 7 times, keeping track of the winning numbers.

Accepted Answer

A)  Not binomial: the trials are not independent. 
B)  Not binomial: there are more than two outcomes for each trial. 
C)  Not binomial: there are too many trials. 
D)  The procedure results in a binomial distribution.

Question 16

For the table shown below, the random variable x is the number of males with tinnitus (ringing ears)among four randomly selected males, based on a medical journal. Find the mean and standard deviation for the random variable x. Use the range rule of thumb to identify the range of values that are not significant for the number of males with tinnitus among four randomly selected males. Is getting three males with tinnitus among four randomly selected males a significantly high number?
 $\begin{array} { c | c } 
\boldsymbol { x } & \boldsymbol { P } ( \boldsymbol { x } ) \
\hline 0 & 0.674 \
1 & 0.280 \
2 & 0.044 \
3 & 0.003 \
4 & 0 +
\end{array}$

Accepted Answer

The answer of For the table shown below, the random...

Question 17

Helene claimed that the expected value when rolling a fair die was 3.5. Steve said that wasn't possible. He said that the expected value was the most likely value in a single roll of
the die, and since it wasn't possible for a die to turn up with a value of 3.5, the expected value
couldn't possibly be 3.5. Who is right?

Accepted Answer

The answer of Helene claimed that the expected value when...

Question 18

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. 
$\begin{array} { c | c } 
\boldsymbol { x } & \boldsymbol { P } ( \boldsymbol { x } ) \
\hline 0 & 0.1296 \
1 & 0.3456 \
2 & 0.3456 \
3 & 0.1536 \
4 & 0.0256
\end{array}$

Accepted Answer

The answer of Determine whether the following is a probability...

Question 19

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.

Accepted Answer

A)  3.5 students 
B)  2.8 students 
C)  4.0 students 
D)  0.2 students

Question 20

Suppose that weight of adolescents is being studied by a health organization and that the accompanying tables describes the probability distribution for three randomly selected adolescents, where x is the number who are considered morbidly obese. Is it significant to
Have no obese subjects among three randomly selected adolescents? $\begin{array}{c|c}
\boldsymbol{x} & \boldsymbol{P}(\boldsymbol{x}) \
\hline 0 & 0.111 \
1 & 0.215 \
2 & 0.450 \
3 & 0.224
\end{array}$

Accepted Answer

A)  $\mathrm { Yes }$ 
B)  No

Exam 5: Discrete Probability Distributions

A company manufactures batteries in batches of 6 and there is a 3% rate of defects. Find the mean number of defects per batch.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 9 times, keeping track of the occurrences of a winning number of "16) "

In a certain town, 22% of voters favor a given ballot measure. For groups of 21 voters, find the variance for the number who favor the measure.

A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in? Assume that each serve is independent of the others.

Do probability distributions measure what did happen or what will probably happen? How do we use probability distributions to make decisions?

Find the mean, $\mu$ for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n=676 ; p=0.7

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

Sampling without replacement involves dependent events, so this would not be considered a binomial experiment. Explain the circumstances under which sampling without replacement could be considered independent and, thus, binomial.

The probability that a call received by a certain switchboard will be a wrong number is 0.02. Use the Poisson distribution to approximate the probability that among 150 calls received by the switchboard, there are at least two wrong numbers. Round your answer to four Decimal places.

Find the standard deviation, $\sigma$ , for the binomial distribution which has n=48 and $p = 3 / 5$ Round your answer to the nearest hundredth.

Identify the given random variable as being discrete or continuous. The cost of a randomly selected orange.

On a multiple choice test with 17 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.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 7 times, keeping track of the winning numbers.

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. $\begin{array} { c | c } \boldsymbol { x } & \boldsymbol { P } ( \boldsymbol { x } ) \\\hline 0 & 0.1296 \\1 & 0.3456 \\2 & 0.3456 \\3 & 0.1536 \\4 & 0.0256\end{array}$

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.

Exam 5: Discrete Probability Distributions

A company manufactures batteries in batches of 6 and there is a 3% rate of defects. Find the mean number of defects per batch.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 9 times, keeping track of the occurrences of a winning number of "16) "

In a certain town, 22% of voters favor a given ballot measure. For groups of 21 voters, find the variance for the number who favor the measure.

A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in? Assume that each serve is independent of the others.

Do probability distributions measure what did happen or what will probably happen? How do we use probability distributions to make decisions?

Find the mean, μ\muμ for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n=676 ; p=0.7

A die is rolled nine times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

Sampling without replacement involves dependent events, so this would not be considered a binomial experiment. Explain the circumstances under which sampling without replacement could be considered independent and, thus, binomial.

The probability that a call received by a certain switchboard will be a wrong number is 0.02. Use the Poisson distribution to approximate the probability that among 150 calls received by the switchboard, there are at least two wrong numbers. Round your answer to four Decimal places.

Find the standard deviation, σ\sigmaσ , for the binomial distribution which has n=48 and p=3/5p = 3 / 5p=3/5 Round your answer to the nearest hundredth.

Identify the given random variable as being discrete or continuous. The cost of a randomly selected orange.

On a multiple choice test with 17 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.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Spinning a roulette wheel 7 times, keeping track of the winning numbers.

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.

Find the mean, $\mu$ for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n=676 ; p=0.7

Find the standard deviation, $\sigma$ , for the binomial distribution which has n=48 and $p = 3 / 5$ Round your answer to the nearest hundredth.