Question 1

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

A)  0.1 
B)  0.3 
C)  0.6 
D)  32 
A)  0.1 
B)  0.3 
C)  0.6 
D)  32

Question 2

In a certain town, 90 percent of voters are in favor of a given ballot measure and 10 percent are opposed. For groups of 260 voters, find the mean for the number who oppose the measure.

Accepted Answer

A)  26 
B)  90 
C)  10 
D)  234 
A)  26 
B)  90 
C)  10 
D)  234

Question 3

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. $$\begin{array}{l}
\text {\quad\quad\quad\quad\quad\quad\quad\quad Probabilities of Girls }\
\begin{array} { c | c | c | c | c | c } 
x ( \text { girls) } & P ( x ) & x \text { (girls) } & P ( x ) & x \text { (girls) } & P ( x ) \
\hline 0 & 0.000 & 5 & 0.122 & 10 & 0.061 \
1 & 0.001 & 6 & 0.183 & 11 & 0.022 \
2 & 0.006 & 7 & 0.209 & 12 & 0.006 \
3 & 0.022 & 8 & 0.183 & 13 & 0.001 \
4 & 0.061 & 9 & 0.122 & 14 & 0.000
\end{array}
\end{array}$$
-Find the probability of selecting 12 or more girls.

Accepted Answer

A)  0.007 
B)  0.006 
C)  0.022 
D)  0.001 
A)  0.007 
B)  0.006 
C)  0.022 
D)  0.001

Question 4

Provide an appropriate response. Round to the nearest hundredth.
-The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.6561, 0.2916, 0.0486, 0.0036, and 0.0001, respectively. Find the standard deviation for the probability distribution.

Accepted Answer

A)  $\sigma = 0.60$ 
B)  $\sigma = 0.36$ 
C)  $\sigma = 0.72$ 
D)  $\sigma = 0.53$ 
A)  $\sigma = 0.60$ 
B)  $\sigma = 0.36$ 
C)  $\sigma = 0.72$ 
D)  $\sigma = 0.53$

Question 5

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.
-$$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.15 \
1 & 0.33 \
2 & 0.22 \
3 & 0.28 \
4 & 0.02
\end{array}$$

Accepted Answer

Probabilit

Question 6

An experiment of a gender selection method includes a control group of 8 couples who are not given any treatment intended to influence the genders of their babies. Construct a table listing the possible values of the random variable x (which represents the number of girls among the 8 births) and the corresponding probabilities. Then find the mean and standard deviation for the number of girls in such groups of 10 and the maximum and minimum usual values for the number of girls. Round all results to four decimal places.

Accepted Answer

None

Question 7

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-Spinning a roulette wheel 6 times, keeping track of the occurrences of a winning number of "16".

Accepted Answer

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

Question 8

Determine whether the given procedure results in a binomial distribution. If not, state the reason why.
-Choosing 5 people (without replacement) from a group of 23 people, of which 15 are women, keeping track of the number of men chosen.

Accepted Answer

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

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.

Accepted Answer

A)  0.0065 
B)  0.0045 
C)  0.0055 
D)  0.0035 
A)  0.0065 
B)  0.0045 
C)  0.0055 
D)  0.0035

Question 10

Find the standard deviation, ?, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth.
-$\mathrm { n } = 693 ; \mathrm { p } = 0.7$

Accepted Answer

A)  $\sigma = 16.18$ 
B)  $\sigma = 9.65$ 
C)  $\sigma = 12.06$ 
D)  $\sigma = 15.33$ 
A)  $\sigma = 16.18$ 
B)  $\sigma = 9.65$ 
C)  $\sigma = 12.06$ 
D)  $\sigma = 15.33$

Question 11

A die is rolled 19 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the number of twos.

Accepted Answer

A)  2.2 
B)  15.8 
C)  4.8 
D)  1.6 
A)  2.2 
B)  15.8 
C)  4.8 
D)  1.6

Question 12

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.
-$$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 1 & 0.037 \
2 & 0.200 \
3 & 0.444 \
4 & 0.296
\end{array}$$

Accepted Answer

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

Question 13

A die is rolled 9 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)  3 
B)  2.25 
C)  7.5 
D)  1.5 
A)  3 
B)  2.25 
C)  7.5 
D)  1.5

Question 14

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

A)  48.8 
B)  23.8 
C)  2.2 
D)  4.9 
A)  48.8 
B)  23.8 
C)  2.2 
D)  4.9

Question 15

The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. Suppose we have three types of mutually exclusive outcomes denoted by $\mathrm { A } , \mathrm { B }$, and $\mathrm { C }$. Let $\mathrm { P } ( \mathrm { A } ) = \mathrm { p } _ { 1 } , \mathrm { P } ( \mathrm { B } ) = \mathrm { p } _ { 2 } , \mathrm { P } ( \mathrm { C } ) = \mathrm { p } _ { 3 }$. In $n$ independent trials, the probability of $\mathrm { x } _ { 1 }$ outcomes of type $\mathrm { A } , \mathrm { x } _ { 2 }$ outcomes of type $\mathrm { B }$, and $\mathrm { x } _ { 3 }$ outcomes of type $\mathrm { C }$ is given by
$$\frac { n ! } { \left( x _ { 1 } \right) ! \left( x _ { 2 } \right) ! \left( x _ { 3 } \right) ! } \cdot p _ { 1 } { } ^ { x _ { 1 } } \cdot p _ { 2 } { } ^ { x _ { 2 } } \cdot p _ { 3 } { } ^ { x _ { 3 } }$$ A genetics experiment involves four mutually exclusive genotypes identified as A, B, C, and D, and they are all equally likely. If 13 offspring are tested, find the probability of getting exactly 3 A's,2 B's,3 C's, and 5 D's by expanding the above expression so that it applies to four types of outcomes instead of only three. Round your answer to five decimal places.

Accepted Answer

A)  1.28875 
B)  0.01074 
C)  0.00268 
D)  0.04296 
A)  1.28875 
B)  0.01074 
C)  0.00268 
D)  0.04296

Question 16

A company manufactures batteries in batches of 25 and there is a 3% rate of defects. Find the mean number of defects per batch.

Accepted Answer

A)  24.3 
B)  0.8 
C)  7.5 
D)  75 
A)  24.3 
B)  0.8 
C)  7.5 
D)  75

Question 17

Provide an appropriate response. Round to the nearest hundredth.
-Find the standard deviation for the given probability distribution.

$\begin{array}{c|c}
x & P(x) \
\hline 0 & 0.19 \
1 & 0.26 \
2 & 0.18 \
3 & 0.24 \
4 & 0.13
\end{array}$

Accepted Answer

A)  $\sigma = 1.40$ 
B)  $\sigma = 2.28$ 
C)  $\sigma = 1.76$ 
D)  $\sigma = 1.33$ 
A)  $\sigma = 1.40$ 
B)  $\sigma = 2.28$ 
C)  $\sigma = 1.76$ 
D)  $\sigma = 1.33$

Question 18

Suppose that voting in municipal elections is being studied and that the accompanying tables describes the probability distribution for four randomly selected people, where x is the number that voted in the last election. Is it unusual to find four voters among four randomly selected people? 
$$\begin{array} { c | c } 
\mathrm { x } & \mathrm { P } ( \mathrm { x } ) \
\hline 0 & 0.23 \
1 & 0.32 \
2 & 0.26 \
3 & 0.15 \
4 & 0.04
\end{array}$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 19

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

Accepted Answer

A)  1.9 
B)  2.6 
C)  1.7 
D)  3.5 
A)  1.9 
B)  2.6 
C)  1.7 
D)  3.5

Question 20

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? $$\begin{array} { r | r } 
\text { Outcome } & \text { Probability } \
\hline \text { Red } & .02 \
\text { Blue } & .04 \
\text { Yellow } & .16 \
\text { White } & .78
\end{array}$$

Accepted Answer

The expected winning

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.

In a certain town, 90 percent of voters are in favor of a given ballot measure and 10 percent are opposed. For groups of 260 voters, find the mean for the number who oppose the measure.

Provide an appropriate response. Round to the nearest hundredth. -The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.6561, 0.2916, 0.0486, 0.0036, and 0.0001, respectively. Find the standard deviation for the probability distribution.

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. - () 0 0.15 1 0.33 2 0.22 3 0.28 4 0.02

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Spinning a roulette wheel 6 times, keeping track of the occurrences of a winning number of "16".

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Choosing 5 people (without replacement) from a group of 23 people, of which 15 are women, keeping track of the number of men chosen.

Find the standard deviation, ?, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 693 ; \mathrm { p } = 0.7$

A die is rolled 19 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the number of twos.

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. - () 1 0.037 2 0.200 3 0.444 4 0.296

A die is rolled 9 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.

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.

A company manufactures batteries in batches of 25 and there is a 3% rate of defects. Find the mean number of defects per batch.

Provide an appropriate response. Round to the nearest hundredth. -Find the standard deviation for the given probability distribution. x P(x) 0 0.19 1 0.26 2 0.18 3 0.24 4 0.13

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

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Normal Probability Distributions

Estimates and Sample Size

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Chi-Square and Analysis of Variance

Filters

Exam 5: Discrete Probability Distributions

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.

In a certain town, 90 percent of voters are in favor of a given ballot measure and 10 percent are opposed. For groups of 260 voters, find the mean for the number who oppose the measure.

Provide an appropriate response. Round to the nearest hundredth. -The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.6561, 0.2916, 0.0486, 0.0036, and 0.0001, respectively. Find the standard deviation for the probability distribution.

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. - () 0 0.15 1 0.33 2 0.22 3 0.28 4 0.02

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Spinning a roulette wheel 6 times, keeping track of the occurrences of a winning number of "16".

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Choosing 5 people (without replacement) from a group of 23 people, of which 15 are women, keeping track of the number of men chosen.

Find the standard deviation, ?, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - n=693;p=0.7\mathrm { n } = 693 ; \mathrm { p } = 0.7n=693;p=0.7

A die is rolled 19 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the number of twos.

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. - () 1 0.037 2 0.200 3 0.444 4 0.296

A die is rolled 9 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.

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.

A company manufactures batteries in batches of 25 and there is a 3% rate of defects. Find the mean number of defects per batch.

Provide an appropriate response. Round to the nearest hundredth. -Find the standard deviation for the given probability distribution. x P(x) 0 0.19 1 0.26 2 0.18 3 0.24 4 0.13

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

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Normal Probability Distributions

Estimates and Sample Size

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Chi-Square and Analysis of Variance

Filters

Find the standard deviation, ?, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 693 ; \mathrm { p } = 0.7$