Question 1

The probabilities that a customer entering a particular bookstore buys 0, 1, 2, 3, 4, or 5 books are 0.30, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively.
-For the probability distribution above, find the variance.

Accepted Answer

The answer of The probabilities that a customer entering a...

Question 2

The probabilities that a customer entering a particular bookstore buys 0, 1, 2, 3, 4, or 5 books are 0.30, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively.
-For the probability distribution above, find the standard deviation.

Accepted Answer

The answer of The probabilities that a customer entering a...

Question 3

The probabilities of getting $0,1,2$, or 3 heads in three flips of a balanced coin are, respectively, $\frac{1}{8}, \frac{3}{8}, \frac{3}{8}$, and $\frac{1}{8}$.
Use the formulas that define $\mu$ and $\sigma^{2}$ to find the mean and the standard deviation of this probability distribution. If necessary, round to the nearest thousandth.

Accepted Answer

The answer of The probabilities of getting $0,1,2$, or 3...

Question 4

Find the mean and standard deviation of the number of tails obtained in 576 flips of a balanced coin using the fact that $\mathrm{x}$ is a binomial random variable. If necessary, round to the nearest thousandth.

Accepted Answer

The answer of Find the mean and standard deviation of...

Question 5

Find the mean and standard deviation of the number of defectives in a sample of 700 parts made by a machine, when the probability is 0.05 that any one of the parts is defective. Use the fact that $\mathrm{x}$ is a binomial random variable. If necessary, round to the nearest thousandth.

Accepted Answer

The answer of Find the mean and standard deviation of...

Question 6

The daily number of people who examine cars in a particular automobile showroom is a random variable with $\mu=80$ and $\sigma=6$.
-According to Chebyshev's theorem, with what probability can we claim that between 68 and 92 people will look at cars in the showroom on a particular day?

Accepted Answer

The answer of The daily number of people who examine...

Question 7

The daily number of people who examine cars in a particular automobile showroom is a random variable with $\mu=80$ and $\sigma=6$.
-Give the interval such that there is at least $35 / 36$ probability that the number of people who look at cars will be in that interval.

Accepted Answer

The answer of The daily number of people who examine...

Question 8

The editor of a particular women's magazine claims that the magazine is read by $60 \%$ of the female students on a college campus.
-If the above claim is true, find the probability that in a random sample of 10 female students more than two read the magazine.

Accepted Answer

The answer of The editor of a particular women's magazine...

Question 9

The editor of a particular women's magazine claims that the magazine is read by $60 \%$ of the female students on a college campus.
-If the above claim is true, find the probability that in a random sample of 10 female students exactly six read the magazine.

Accepted Answer

The answer of The editor of a particular women's magazine...

Question 10

The editor of a particular women's magazine claims that the magazine is read by $60 \%$ of the female students on a college campus.
-If the above is true, find the probability that in a random sample of 10 female students at most two read the magazine.

Accepted Answer

The answer of The editor of a particular women's magazine...

Question 11

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur.
-At least three bounce.

Accepted Answer

The answer of If $2 \%$ of the checks received...

Question 12

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur.
-At most two bounce.

Accepted Answer

The answer of If $2 \%$ of the checks received...

Question 13

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur.
-Exactly 96 do not bounce.

Accepted Answer

The answer of If $2 \%$ of the checks received...

Question 14

Among 10 videotapes that a retail store has available, four are comedies. If a customer selects three videotapes at random to buy for a friend, find the probability that: the following will occur.
-None of them are comedies.

Accepted Answer

The answer of Among 10 videotapes that a retail store...

Question 15

Among 10 videotapes that a retail store has available, four are comedies. If a customer selects three videotapes at random to buy for a friend, find the probability that: the following will occur.
-Two of them are comedies.

Accepted Answer

The answer of Among 10 videotapes that a retail store...

Question 16

Tell whether the given function can serve as the probability distribution of an appropriate random variable.
-f(x)=$\frac{1}{5}$ for $x=0,1,2,3,4$

Accepted Answer

The function assigns a probability of $\frac{1}{5}$ to each of the five possible outcomes (0, 1, 2, 3, 4), and the sum of these probabilities is 1, satisfying the conditions for a probability distribution.

Question 17

Tell whether the given function can serve as the probability distribution of an appropriate random variable.
-f(1)=0.25, f(2)=0.40, f(3)=0.30

Accepted Answer

The answer of Tell whether the given function can serve...

Question 18

The Poisson distribution can be applied in situations which do not involve the binomial distribution.

Accepted Answer

The Poisson distribution is used for modeling the number of times an event occurs in a fixed interval of time or space, and it applies to scenarios where events occur independently and the rate at which they occur is constant, which is different from the binomial distribution that requires a fixed number of trials and a constant probability of success in each trial.

Question 19

The hypergeometric distribution with $n=150, a=20$, and $b=2180$ can be approximated with a Poisson distribution.

Accepted Answer

Given the large population size ($b=2180$) and the relatively small sample size ($n=150$) and success states ($a=20$), the conditions for approximating the hypergeometric distribution with a Poisson distribution are met, especially since $n$ is much smaller than $N=a+b$, and $a/N$ is small.

Question 20

The mean of a probability distribution is always a value that can be obtained by the random variable.

Accepted Answer

The mean of a probability distribution, also known as the expected value, is a weighted average of all possible values. This does not necessarily have to be a value that the random variable can take. For example, in a fair dice roll, the expected value is 3.5, which is not a possible outcome of the roll.

Quiz 8: Probability Distributions

The probabilities that a customer entering a particular bookstore buys 0, 1, 2, 3, 4, or 5 books are 0.30, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively. -For the probability distribution above, find the variance.

The probabilities that a customer entering a particular bookstore buys 0, 1, 2, 3, 4, or 5 books are 0.30, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively. -For the probability distribution above, find the standard deviation.

Find the mean and standard deviation of the number of tails obtained in 576 flips of a balanced coin using the fact that $\mathrm{x}$ is a binomial random variable. If necessary, round to the nearest thousandth.

Find the mean and standard deviation of the number of defectives in a sample of 700 parts made by a machine, when the probability is 0.05 that any one of the parts is defective. Use the fact that $\mathrm{x}$ is a binomial random variable. If necessary, round to the nearest thousandth.

The daily number of people who examine cars in a particular automobile showroom is a random variable with $\mu=80$ and $\sigma=6$ . -According to Chebyshev's theorem, with what probability can we claim that between 68 and 92 people will look at cars in the showroom on a particular day?

The daily number of people who examine cars in a particular automobile showroom is a random variable with $\mu=80$ and $\sigma=6$ . -Give the interval such that there is at least $35 / 36$ probability that the number of people who look at cars will be in that interval.

The editor of a particular women's magazine claims that the magazine is read by $60 \%$ of the female students on a college campus. -If the above claim is true, find the probability that in a random sample of 10 female students more than two read the magazine.

The editor of a particular women's magazine claims that the magazine is read by $60 \%$ of the female students on a college campus. -If the above claim is true, find the probability that in a random sample of 10 female students exactly six read the magazine.

The editor of a particular women's magazine claims that the magazine is read by $60 \%$ of the female students on a college campus. -If the above is true, find the probability that in a random sample of 10 female students at most two read the magazine.

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -At least three bounce.

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -At most two bounce.

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -Exactly 96 do not bounce.

Among 10 videotapes that a retail store has available, four are comedies. If a customer selects three videotapes at random to buy for a friend, find the probability that: the following will occur. -None of them are comedies.

Among 10 videotapes that a retail store has available, four are comedies. If a customer selects three videotapes at random to buy for a friend, find the probability that: the following will occur. -Two of them are comedies.

Tell whether the given function can serve as the probability distribution of an appropriate random variable. -f(x)= $\frac{1}{5}$ for $x=0,1,2,3,4$

Tell whether the given function can serve as the probability distribution of an appropriate random variable. -f(1)=0.25, f(2)=0.40, f(3)=0.30

The Poisson distribution can be applied in situations which do not involve the binomial distribution.

The hypergeometric distribution with $n=150, a=20$ , and $b=2180$ can be approximated with a Poisson distribution.

The mean of a probability distribution is always a value that can be obtained by the random variable.

Quiz 8: Probability Distributions

The probabilities that a customer entering a particular bookstore buys 0, 1, 2, 3, 4, or 5 books are 0.30, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively. -For the probability distribution above, find the variance.

The probabilities that a customer entering a particular bookstore buys 0, 1, 2, 3, 4, or 5 books are 0.30, 0.20, 0.20, 0.15, 0.10, and 0.05 respectively. -For the probability distribution above, find the standard deviation.

Find the mean and standard deviation of the number of tails obtained in 576 flips of a balanced coin using the fact that x\mathrm{x}x is a binomial random variable. If necessary, round to the nearest thousandth.

Find the mean and standard deviation of the number of defectives in a sample of 700 parts made by a machine, when the probability is 0.05 that any one of the parts is defective. Use the fact that x\mathrm{x}x is a binomial random variable. If necessary, round to the nearest thousandth.

The daily number of people who examine cars in a particular automobile showroom is a random variable with μ=80\mu=80μ=80 and σ=6\sigma=6σ=6 . -Give the interval such that there is at least 35/3635 / 3635/36 probability that the number of people who look at cars will be in that interval.

The editor of a particular women's magazine claims that the magazine is read by 60%60 \%60% of the female students on a college campus. -If the above claim is true, find the probability that in a random sample of 10 female students more than two read the magazine.

The editor of a particular women's magazine claims that the magazine is read by 60%60 \%60% of the female students on a college campus. -If the above claim is true, find the probability that in a random sample of 10 female students exactly six read the magazine.

The editor of a particular women's magazine claims that the magazine is read by 60%60 \%60% of the female students on a college campus. -If the above is true, find the probability that in a random sample of 10 female students at most two read the magazine.

If 2%2 \%2% of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -At least three bounce.

If 2%2 \%2% of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -At most two bounce.

If 2%2 \%2% of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -Exactly 96 do not bounce.

Among 10 videotapes that a retail store has available, four are comedies. If a customer selects three videotapes at random to buy for a friend, find the probability that: the following will occur. -None of them are comedies.

Among 10 videotapes that a retail store has available, four are comedies. If a customer selects three videotapes at random to buy for a friend, find the probability that: the following will occur. -Two of them are comedies.

Tell whether the given function can serve as the probability distribution of an appropriate random variable. -f(x)= 15\frac{1}{5}51​ for x=0,1,2,3,4x=0,1,2,3,4x=0,1,2,3,4

Tell whether the given function can serve as the probability distribution of an appropriate random variable. -f(1)=0.25, f(2)=0.40, f(3)=0.30

The Poisson distribution can be applied in situations which do not involve the binomial distribution.

The hypergeometric distribution with n=150,a=20n=150, a=20n=150,a=20 , and b=2180b=2180b=2180 can be approximated with a Poisson distribution.

The mean of a probability distribution is always a value that can be obtained by the random variable.

Find the mean and standard deviation of the number of tails obtained in 576 flips of a balanced coin using the fact that $\mathrm{x}$ is a binomial random variable. If necessary, round to the nearest thousandth.

Find the mean and standard deviation of the number of defectives in a sample of 700 parts made by a machine, when the probability is 0.05 that any one of the parts is defective. Use the fact that $\mathrm{x}$ is a binomial random variable. If necessary, round to the nearest thousandth.

The daily number of people who examine cars in a particular automobile showroom is a random variable with $\mu=80$ and $\sigma=6$ . -Give the interval such that there is at least $35 / 36$ probability that the number of people who look at cars will be in that interval.

The editor of a particular women's magazine claims that the magazine is read by $60 \%$ of the female students on a college campus. -If the above claim is true, find the probability that in a random sample of 10 female students more than two read the magazine.

The editor of a particular women's magazine claims that the magazine is read by $60 \%$ of the female students on a college campus. -If the above claim is true, find the probability that in a random sample of 10 female students exactly six read the magazine.

The editor of a particular women's magazine claims that the magazine is read by $60 \%$ of the female students on a college campus. -If the above is true, find the probability that in a random sample of 10 female students at most two read the magazine.

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -At least three bounce.

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -At most two bounce.

If $2 \%$ of the checks received in an all night drugstore bounce, find the probability that in the next 100 checks received by the store, the following will occur. -Exactly 96 do not bounce.

Tell whether the given function can serve as the probability distribution of an appropriate random variable. -f(x)= $\frac{1}{5}$ for $x=0,1,2,3,4$

The hypergeometric distribution with $n=150, a=20$ , and $b=2180$ can be approximated with a Poisson distribution.