Question 1

Egyptian
Let x represent the number of children in an Egyptian household.The probability distribution of x is as follows: $$\begin{array} { l | c c c c c } 
x & 1 & 2 & 3 & 4 & 5 \
\hline p ( x ) & 0.25 & 0.33 & 0.17 & 0.15 & 0.10
\end{array}$$
-What is the probability that a randomly selected Egyptian household will have between 2 and 4 children?

Accepted Answer

The answer of Egyptian
Let x represent the number of children...

Question 2

An urn contains 5 red marbles and 5 green ones.Two marbles are selected without replacement.What is the probability that both marbles are red?

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The answer of An urn contains 5 red marbles and...

Question 3

An urn contains 5 red marbles and 5 green ones.Two marbles are selected without replacement.What is the probability that at least one marble is red?

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Question 4

Egyptian
Let x represent the number of children in an Egyptian household.The probability distribution of x is as follows: $$\begin{array} { l | c c c c c } 
x & 1 & 2 & 3 & 4 & 5 \
\hline p ( x ) & 0.25 & 0.33 & 0.17 & 0.15 & 0.10
\end{array}$$
-Find the standard deviation of the number of children in an Egyptian household.

Accepted Answer

The answer of Egyptian
Let x represent the number of children...

Question 5

Egyptian
Let x represent the number of children in an Egyptian household.The probability distribution of x is as follows: $$\begin{array} { l | c c c c c } 
x & 1 & 2 & 3 & 4 & 5 \
\hline p ( x ) & 0.25 & 0.33 & 0.17 & 0.15 & 0.10
\end{array}$$
-What is the probability that a randomly selected Egyptian household will have fewer than 4 children?

Accepted Answer

The answer of Egyptian
Let x represent the number of children...

Question 6

Egyptian
Let x represent the number of children in an Egyptian household.The probability distribution of x is as follows: $$\begin{array} { l | c c c c c } 
x & 1 & 2 & 3 & 4 & 5 \
\hline p ( x ) & 0.25 & 0.33 & 0.17 & 0.15 & 0.10
\end{array}$$
-Find the expected number of children in a randomly selected Egyptian household.

Accepted Answer

The answer of Egyptian
Let x represent the number of children...

Question 7

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute.
-A cashier at Carter's cafeteria can total an average of 2.2 trays per minute.The probability that the cashier will total no more than three trays in a minute is:

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Question 8

The Poisson random variable is a:

Accepted Answer

The Poisson random variable is a discrete random variable that can take infinitely many possible values. It models the number of events occurring in a fixed time interval or space when the events occur independently and at a constant rate. The possible values the Poisson random variable can take are 0, 1, 2, 3, and so on, and there is no finite upper limit on the number of events that can occur.

Question 9

Which of the following events is best described using a hypergeometric distribution?

Accepted Answer

The hypergeometric distribution is used when the population is not large enough for the binomial distribution to be appropriate, and when sampling is done without replacement. Option C fits this description, as we are sampling without replacement from a small population of 25 individuals to select a certain number of male jurors.

Question 10

As a rule of thumb,a binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, $\pi$ ,is:

Accepted Answer

A binomial distribution can be approximated by a Poisson distribution when the number of trials is large and the probability of success is small (typically smaller than 0.05). This is because the Poisson distribution is a limit of the binomial distribution as the number of trials goes to infinity while the expected number of successes remains constant.

Question 11

MBI Co.
The MBI Company found that at the end of each month,2% of its two million accounting entries contained errors.Today,one operator has made 50 computer entries.
What is the probability that at most two errors were made?

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The answer of MBI Co.
The MBI Company found that at...

Question 12

Chocolates
A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random.
-What is the probability that exactly 2 pieces have nuts?

Accepted Answer

The probability of choosing exactly 2 pieces with nuts can be calculated using combinations. The number of ways to choose 2 pieces with nuts out of 10 is $C(10,2)$, and the number of ways to choose 2 pieces without nuts out of 8 is $C(8,2)$. The total number of ways to choose 4 pieces out of 18 is $C(18,4)$. Thus, the probability is $\frac{C(10,2) \times C(8,2)}{C(18,4)} = \frac{45 \times 28}{3060} = 0.412$.

Question 13

A high school play has five roles to fill with students.Seven girls and nine boys have expressed an interest in the play.What is the probability that exactly 0 girls will be selected?

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The answer of A high school play has five roles...

Question 14

Chocolates
A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random.
-What is the probability that at least 3 pieces have nuts?

Accepted Answer

The probability of choosing a piece with nuts is 10/18, and the probability of choosing a piece without nuts is 8/18. The probability of choosing at least 3 pieces with nuts is the complement of the probability of choosing 0, 1, or 2 pieces with nuts. The probability of choosing 0 pieces with nuts is (8/18)^4, the probability of choosing 1 piece with nuts is 4 * (10/18) * (8/18)^3, and the probability of choosing 2 pieces with nuts is 6 * (10/18)^2 * (8/18)^2. Therefore, the probability of choosing at least 3 pieces with nuts is 1 - (8/18)^4 - 4 * (10/18) * (8/18)^3 - 6 * (10/18)^2 * (8/18)^2 = 0.382.

Question 15

A committee of eight politicians needs to be chosen from 11 Democrats and 15 Republicans.What is the probability that exactly 2 Democrats will be selected for the committee?

Accepted Answer

The answer of A committee of eight politicians needs to...

Question 16

A high school play has five roles to fill with students.Seven girls and nine boys have expressed an interest in the play.What is the probability that exactly 3 girls will be selected?

Accepted Answer

The answer of A high school play has five roles...

Question 17

The number of vacancies at a Gulf Shore resort motel on a day during weekends through the tourist season has the following probability distribution: $$\begin{array} { | c | c | } 
\hline \text { Number of Vacancies } & \text { Probability } \
\boldsymbol { x } & \boldsymbol { P } ( \boldsymbol { x } ) \
\hline 0 & 0.29 \
1 & 0.18 \
2 & 0.15 \
3 & 0.13 \
4 & 0.11 \
5 & 0.08 \
6 & 0.06 \
\hline
\end{array}$$ If the mean is 2.07,compute the variance of this distribution.

Accepted Answer

The answer of The number of vacancies at a Gulf...

Question 18

Chocolates
A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random.
-What is the probability that no more than one piece has nuts?

Accepted Answer

The probability of choosing no more than one piece with nuts involves calculating the probabilities of choosing no nuts and exactly one nut, then adding them together. For no nuts, it's (8C4)/(18C4). For exactly one nut, it's (10C1)*(8C3)/(18C4). Adding these probabilities gives approximately 0.206.

Question 19

Egyptian
Let x represent the number of children in an Egyptian household.The probability distribution of x is as follows: $$\begin{array} { l | c c c c c } 
x & 1 & 2 & 3 & 4 & 5 \
\hline p ( x ) & 0.25 & 0.33 & 0.17 & 0.15 & 0.10
\end{array}$$
-What is the probability that a randomly selected Egyptian household will have more than 2 children?

Accepted Answer

The answer of Egyptian
Let x represent the number of children...

Question 20

A committee of eight politicians needs to be chosen from 11 Democrats and 15 Republicans.What is the probability that at least 5 Democrats will be selected for the committee?

Accepted Answer

The answer of A committee of eight politicians needs to...

Quiz 6: Discrete Probability Distributions

An urn contains 5 red marbles and 5 green ones.Two marbles are selected without replacement.What is the probability that both marbles are red?

An urn contains 5 red marbles and 5 green ones.Two marbles are selected without replacement.What is the probability that at least one marble is red?

A cashier at Carter's cafeteria can total an average of 2.2 trays per minute. -A cashier at Carter's cafeteria can total an average of 2.2 trays per minute.The probability that the cashier will total no more than three trays in a minute is:

The Poisson random variable is a:

Which of the following events is best described using a hypergeometric distribution?

As a rule of thumb,a binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, π\piπ ,is:

MBI Co. The MBI Company found that at the end of each month,2% of its two million accounting entries contained errors.Today,one operator has made 50 computer entries. What is the probability that at most two errors were made?

Chocolates A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random. -What is the probability that exactly 2 pieces have nuts?

A high school play has five roles to fill with students.Seven girls and nine boys have expressed an interest in the play.What is the probability that exactly 0 girls will be selected?

Chocolates A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random. -What is the probability that at least 3 pieces have nuts?

A committee of eight politicians needs to be chosen from 11 Democrats and 15 Republicans.What is the probability that exactly 2 Democrats will be selected for the committee?

A high school play has five roles to fill with students.Seven girls and nine boys have expressed an interest in the play.What is the probability that exactly 3 girls will be selected?

Chocolates A box of chocolates contains 18 pieces,10 of which have nuts while the remaining 8 do not.Four pieces are chosen at random. -What is the probability that no more than one piece has nuts?

A committee of eight politicians needs to be chosen from 11 Democrats and 15 Republicans.What is the probability that at least 5 Democrats will be selected for the committee?

As a rule of thumb,a binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, $\pi$ ,is: