Question 1

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 µ - 2? or greater than µ + 2?.
-According to AccuData Media Research, 36% of televisions within the Chicago city limits are tuned to "Eyewitness News" at 5:00 pm on Sunday nights. At 5:00 pm on a given Sunday, 2500 such televisions are randomly selected and checked to determine what is being watched. Would it be
Unusual to find that 959 of the 2500 televisions are tuned to "Eyewitness News"?

Accepted Answer

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

Question 2

Find the mean of the given probability distribution.
-A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.45, 0.37, 0.17, and 0.01, respectively.

Accepted Answer

The answer of Find the mean of the given probability...

Question 3

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.
-$n = 10 , x = 2 , p = \frac { 1 } { 3 }$

Accepted Answer

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

Question 4

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-Rolling a single die 33 times, keeping track of the numbers that are rolled.

Accepted Answer

A binomial distribution requires only two possible outcomes for each trial, but rolling a die results in six possible outcomes.

Question 5

A company manufactures batteries in batches of 11 and there is a 3% rate of defects. Find the standard deviation for the number of defects per batch.

Accepted Answer

The standard deviation for a binomial distribution is calculated using the formula √(n * p * (1-p)), where n is the number of trials (11 batteries), and p is the probability of a defect (0.03). Plugging in the values gives √(11 * 0.03 * 0.97) ≈ 0.6.

Question 6

Identify the given random variable as being discrete or continuous.
-The braking time of a car

Accepted Answer

The braking time of a car can take on any value between 0 seconds and some maximum time. Therefore, it is a continuous random variable.

Question 7

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.
-$\mathrm { n } = 12 , \mathrm { x } = 5 , \mathrm { p } = 0.25$

Accepted Answer

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

Question 8

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 µ - 2? or greater than µ + 2?.
-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 684 consumers who recognize the Dull Computer
Company name?

Accepted Answer

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

Question 9

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.
-$\mathrm { n } = 269 , \mathrm { p } = \frac { 1 } { 3 }$

Accepted Answer

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

Question 10

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.
-$n = 5 , x = 2 , p = 0.70$

Accepted Answer

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

Question 11

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth.
-$\mathrm { n } = 1589 ; \mathrm { p } = 0.57$

Accepted Answer

The answer of Find the mean, µ, for the binomial...

Question 12

In a survey of 300 college graduates, 46% reported that they entered a profession closely related to their college major. If 9 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their
College major?

Accepted Answer

The probability of selecting 3 graduates who entered a profession closely related to their college major is 0.203. This is calculated by multiplying the probability of selecting a graduate who entered a profession closely related to their college major (0.46) by itself 3 times, and then multiplying by the probability of not selecting a graduate who entered a profession closely related to their college major (0.54) 6 times. This gives us the following equation:(0.46)^3 * (0.54)^6 = 0.203

Question 13

Find the mean of the given probability distribution.
-The number of golf balls ordered by customers of a pro shop has the following probability distribution.

$\begin{array}{c|c}
x & P(x) \
\hline 3 & 0.14 \
6 & 0.22 \
9 & 0.36 \
12 & 0.18 \
15 & 0.10
\end{array}$

Accepted Answer

The answer of Find the mean of the given probability...

Question 14

In a certain town, 40% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. Find the standard deviation for the probability distribution.

$\begin{array}{c|c}
\mathrm{x} & \mathrm{P}(\mathrm{x}) \
\hline 0 & 0.1296 \
1 & 0.3456 \
2 & 0.3456 \
3 & 0.1536 \
4 & 0.0256
\end{array}$

Accepted Answer

The answer of In a certain town, 40% of adults...

Question 15

Assume that there is a 0.15 probability that a basketball playoff series will last four games, a 0.30 probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30 probability that it will last seven games. Is it unusual for a team to win a series in 7 games?

Accepted Answer

The probability of the series lasting seven games is 0.30, which is not considered unusual as it is a relatively common outcome compared to the other probabilities given.

Question 16

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 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 480 jawbreakers that weigh more than .4 ounces?

Accepted Answer

The mean number of jawbreakers that weigh more than .4 ounces is 0.6 * 800 = 480. The standard deviation is sqrt(0.6 * 0.4 * 800) = 16.97. So, the range of usual values is 480 +/- 2 * 16.97 = 446.06 to 513.94. Since 480 is within this range, it would not be unusual for this sample of 800 to contain 480 jawbreakers that weigh more than .4 ounces.

Question 17

On a multiple choice test with 27 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the variance for the number of correct answers.

Accepted Answer

The variance for a binomial distribution is calculated using the formula np(1-p), where n is the number of trials (questions) and p is the probability of success (correct answer). Here, n = 27 and p = 1/4. So, variance = 27 * (1/4) * (3/4) = 5.0625, which is approximately 5.1.

Question 18

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using
the table. $$\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad Probabilities of Girls }\
\begin{array} { c | c | c | c | c | c } 
x ( \text { girls } ) & P ( x ) & x \text { (girls) } & P ( x ) & x ( \text { girls } ) & P ( x ) \
\hline 0 & 0.000 & 5 & 0.122 & 10 & 0.061 \
1 & 0.001 & 6 & 0.183 & 11 & 0.022 \
2 & 0.006 & 7 & 0.209 & 12 & 0.006 \
3 & 0.022 & 8 & 0.183 & 13 & 0.001 \
4 & 0.061 & 9 & 0.122 & 14 & 0.000
\end{array}
\end{array}$$
-Find the probability of selecting 2 or more girls.

Accepted Answer

The probability of selecting 2 or more girls is 1 minus the probability of selecting fewer than 2 girls (0 or 1 girl). P(x ≥ 2) = 1 - (P(0) + P(1)) = 1 - (0.000 + 0.001) = 0.999.

Question 19

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth.
-$\mathrm { n } = 38 ; \mathrm { p } = 0.4$

Accepted Answer

The standard deviation for a binomial distribution is calculated using the formula $\sigma = \sqrt{n \cdot p \cdot (1-p)}$. Substituting the given values, $\sigma = \sqrt{38 \cdot 0.4 \cdot 0.6} = \sqrt{9.12} \approx 3.02$.

Question 20

On a multiple choice test with 26 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.

Accepted Answer

The standard deviation for a binomial distribution is calculated using the formula √(n * p * (1-p)), where n is the number of trials (questions) and p is the probability of success (correct answer). Here, n = 26 and p = 1/4. So, the standard deviation is √(26 * 1/4 * 3/4) = √(4.875) ≈ 2.2.

Quiz 5: Discrete Probability Distributions

Find the mean of the given probability distribution. -A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.45, 0.37, 0.17, and 0.01, respectively.

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. - $n = 10 , x = 2 , p = \frac { 1 } { 3 }$

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Rolling a single die 33 times, keeping track of the numbers that are rolled.

A company manufactures batteries in batches of 11 and there is a 3% rate of defects. Find the standard deviation for the number of defects per batch.

Identify the given random variable as being discrete or continuous. -The braking time of a car

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. - $\mathrm { n } = 269 , \mathrm { p } = \frac { 1 } { 3 }$

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. - $n = 5 , x = 2 , p = 0.70$

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 1589 ; \mathrm { p } = 0.57$

Find the mean of the given probability distribution. -The number of golf balls ordered by customers of a pro shop has the following probability distribution. $\begin{array}{c|c}x & P(x) \\\hline 3 & 0.14 \\6 & 0.22 \\9 & 0.36 \\12 & 0.18 \\15 & 0.10\end{array}$

Assume that there is a 0.15 probability that a basketball playoff series will last four games, a 0.30 probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30 probability that it will last seven games. Is it unusual for a team to win a series in 7 games?

On a multiple choice test with 27 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the variance for the number of correct answers.

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 38 ; \mathrm { p } = 0.4$

On a multiple choice test with 26 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.

Quiz 5: Discrete Probability Distributions

Find the mean of the given probability distribution. -A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.45, 0.37, 0.17, and 0.01, respectively.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Rolling a single die 33 times, keeping track of the numbers that are rolled.

A company manufactures batteries in batches of 11 and there is a 3% rate of defects. Find the standard deviation for the number of defects per batch.

Identify the given random variable as being discrete or continuous. -The braking time of a car

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - n=1589;p=0.57\mathrm { n } = 1589 ; \mathrm { p } = 0.57n=1589;p=0.57

Assume that there is a 0.15 probability that a basketball playoff series will last four games, a 0.30 probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30 probability that it will last seven games. Is it unusual for a team to win a series in 7 games?

On a multiple choice test with 27 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the variance for the number of correct answers.

Find the standard deviation, σ\sigmaσ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - n=38;p=0.4\mathrm { n } = 38 ; \mathrm { p } = 0.4n=38;p=0.4

On a multiple choice test with 26 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 1589 ; \mathrm { p } = 0.57$

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 38 ; \mathrm { p } = 0.4$