Question 1

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that 2 or fewer prefer brand C is ________.

Accepted Answer

The answer of Suppose that past history shows that 60%...

Question 2

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that exactly 3 prefer brand C is ________.

Accepted Answer

The answer of Suppose that past history shows that 60%...

Question 3

If π remains constant in a binomial distribution, an increase in n will not change
the mean.

Accepted Answer

The answer of If π remains constant in a binomial...

Question 4

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The expected number of times she will be audited is ________.

Accepted Answer

The answer of In a game called Taxation and Evasion,...

Question 5

If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = ________ .

Accepted Answer

The answer of If X has a binomial distribution with...

Question 6

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The variance of the number that prefer brand C is ________.

Accepted Answer

The answer of Suppose that past history shows that 60%...

Question 7

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that exactly 4 prefer brand C is ________.

Accepted Answer

The answer of Suppose that past history shows that 60%...

Question 8

If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________ .

Accepted Answer

The answer of If X has a binomial distribution with...

Question 9

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The mean number that you would expect to prefer brand C is
________.

Accepted Answer

The answer of Suppose that past history shows that 60%...

Question 10

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The variance of the number of times she will be audited is ________.

Accepted Answer

The answer of In a game called Taxation and Evasion,...

Question 11

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that more than 3 prefer brand C is ________.

Accepted Answer

The answer of Suppose that past history shows that 60%...

Question 12

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that fewer than 2 prefer brand C is ________.

Accepted Answer

The answer of Suppose that past history shows that 60%...

Question 13

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The standard deviation of the number of times she will be audited is ________.

Accepted Answer

The answer of In a game called Taxation and Evasion,...

Question 14

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that at least 1 prefers brand C is ________.

Accepted Answer

The answer of Suppose that past history shows that 60%...

Question 15

Suppose that a judge's decisions follow a binomial distribution and that his verdict
is incorrect 10% of the time. In his next 10 decisions, the probability that he makes fewer than 2
incorrect verdicts is 0.736.

Accepted Answer

We can solve this using the binomial distribution formula:

P(X < 2) = P(X = 0) + P(X = 1)

where X denotes the number of incorrect verdicts in the judge's next 10 decisions. Using the binomial probability formula, we have:

P(X = 0) = (0.9)^10 * (10 choose 0) = 0.3487
P(X = 1) = 10 * (0.1) * (0.9)^9 = 0.3874

Therefore, P(X < 2) = 0.3487 + 0.3874 = 0.7361, which is approximately 0.736.

Therefore, the statement is true and the answer is A.

Question 16

If π remains constant in a binomial distribution, an increase in n will increase the
variance.

Accepted Answer

The variance of a binomial distribution is given by np(1-p), where n is the number of trials and p is the probability of success. If π remains constant and n increases, then p(1-p) remains approximately constant, but np increases, which leads to an increase in the variance.

Question 17

The diameters of 10 randomly selected bolts have a binomial distribution.

Accepted Answer

A binomial distribution requires a fixed number of independent trials with only two possible outcomes (success or failure) for each trial. The diameter of a bolt is a continuous variable, so it cannot have only two possible outcomes. Therefore, the diameters of bolts do not follow a binomial distribution.

Question 18

If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = ________ .

Accepted Answer

The answer of If X has a binomial distribution with...

Question 19

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5
students is to be selected. The probability that exactly 1 prefers brand C is ________.

Accepted Answer

The answer of Suppose that past history shows that 60%...

Question 20

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7,
11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at
rolling the dice. The probability that she gets audited no more than 2 times is ________.

Accepted Answer

The answer of In a game called Taxation and Evasion,...

Quiz 5: Discrete Probability Distributions

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that 2 or fewer prefer brand C is ________.

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 3 prefer brand C is ________.

If π remains constant in a binomial distribution, an increase in n will not change the mean.

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The expected number of times she will be audited is ________.

If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = ________ .

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The variance of the number that prefer brand C is ________.

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 4 prefer brand C is ________.

If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________ .

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The mean number that you would expect to prefer brand C is ________.

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The variance of the number of times she will be audited is ________.

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that more than 3 prefer brand C is ________.

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that fewer than 2 prefer brand C is ________.

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The standard deviation of the number of times she will be audited is ________.

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that at least 1 prefers brand C is ________.

Suppose that a judge's decisions follow a binomial distribution and that his verdict is incorrect 10% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

If π remains constant in a binomial distribution, an increase in n will increase the variance.

The diameters of 10 randomly selected bolts have a binomial distribution.

If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = ________ .

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 1 prefers brand C is ________.

In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited no more than 2 times is ________.