Question 1

A researcher determines that the probability of missing class among students at a local school is p = .16.Assuming that the school has 300 students enrolled,how many students can we expect to miss class on a given day? Hint: This is a binomial probability distribution.
A)252 students
B)48 students
C)16 students
D)There is not enough information to answer this question.

Accepted Answer

Since the probability of missing class among students is p = 0.16, the probability of not missing class is q = 1 - p = 0.84. We can use the binomial probability formula P(X=x) = nCx * p^x * q^(n-x) to calculate the probability of x number of students missing class on a given day, where n = 300 and x can range from 0 to 300. To find the expected number of students who would miss class on a given day, we can multiply the probability of each possible number of students missing class with the number of students. Therefore, the expected number of students who would miss class on a given day is:
E(X) = Σ x * P(X=x) from x = 0 to 300
E(X) = Σ x * nCx * p^x * q^(n-x) from x = 0 to 300
Using a binomial probability calculator, we can find that the expected number of students who would miss class on a given day is approximately 48.

Question 2

A researcher reports that the probability of a college student living on campus is p = .38.If a small local college has 2,000 students enrolled,then what is the standard deviation of college students living on campus? Hint: This is a binomial probability distribution.
A)471.2 students
B)21.7 students
C)760 students
D)There is not enough information to answer this question.

Accepted Answer

The formula for the standard deviation of a binomial distribution is:
σ = √(np(1-p))
where n is the number of trials (students in this case) and p is the probability of success (living on campus in this case).
Plugging in the values, we get:
σ = √(2000 * 0.38 * 0.62) = 21.7
Therefore, the standard deviation of college students living on campus is 21.7 students.

Question 3

A researcher records the number of buckets of popcorn purchased by patrons during one night at the movies.She finds that the probability that a patron purchased 0 buckets of popcorn is p = .27;1 bucket is p = .51;2 buckets is p = .17;and 3 buckets is p = .05.How many buckets of popcorn can we expect a patron to purchase per night at the movies in the long run?
A)exactly 1 bucket of popcorn per night
B)more than 1 bucket of popcorn per night
C)less than one bucket of popcorn per night
D)none of the above

Accepted Answer

The answer of A researcher records the number of buckets...

Question 4

The probability of an outcome can be any positive value.

Accepted Answer

The probability of an outcome must be between 0 and 1, inclusive.

Question 5

Each of the following is an example of a binomial distribution,except
A)the number of heads in ten flips of a fair coin
B)the number of males and females in a sample
C)the number of votes for or against a candidate
D)the time it takes to complete a driving test

Accepted Answer

A binomial distribution requires only two possible outcomes (success or failure) in a fixed number of trials. Option D, the time it takes to complete a driving test, does not fit this criteria as it is a continuous variable and not a discrete count of successes or failures. Options A, B, and C all fit the criteria of a binomial distribution.

Question 6

A researcher determines that the relative frequency of participants with prescription glasses is .23.Hence,the probability that participants will wear prescription glasses must be greater than p = .23.

Accepted Answer

The relative frequency of .23 indicates the proportion of participants with prescription glasses in the sample studied, and it directly estimates the probability (p) of a participant wearing glasses, not necessarily indicating that the probability must be greater than .23.

Question 7

The relative frequency of an outcome is the probability of its occurrence.

Accepted Answer

This statement is true. The relative frequency of an outcome is the number of times it occurs divided by the total number of trials or observations. This is equivalent to the probability of that outcome occurring in future trials.

Question 8

Below is the probability distribution for the number of times students had to take the same exam before passing it.What is the value at the second standard deviation above the mean for this probability distribution? 
A)3.10
B)3.40
C)3.90
D)3.79

Accepted Answer

The answer of Below is the probability distribution for the...

Question 9

If a complimentary outcome has a 1 in 10 chance of occurrence,then the probability of that outcome is p = .10.

Accepted Answer

The statement is correct, as the probability of an event occurring is simply the chance or likelihood of that event occurring. In this case, if a complimentary outcome has a 1 in 10 chance of occurrence, then the probability of that outcome is indeed 0.10 or 10%.

Question 10

If the variance of a probability distribution is 121,then the standard deviation is
A)121
B)21
C)12
D)11

Accepted Answer

The standard deviation is the square root of the variance, so the square root of 121 is 11.

Question 11

Below is the probability distribution for random variable x.What is the standard deviation of this probability distribution? 
A)6.20
B)2.49
C)1.00
D)0.35

Accepted Answer

To calculate the standard deviation, we first need to find the mean of the distribution:

μ = Σ(xi * P(xi)) = (0*0.1)+(1*0.3)+(2*0.2)+(3*0.2)+(4*0.1)+(5*0.1) = 2.2

Next, we can calculate the variance using the formula:
σ^2 = Σ(xi - μ)^2 * P(xi)
= ((0-2.2)^2*0.1)+((1-2.2)^2*0.3)+((2-2.2)^2*0.2)+((3-2.2)^2*0.2)+((4-2.2)^2*0.1)+((5-2.2)^2*0.1)
= 1.96

Finally, we can find the standard deviation by taking the square root of the variance:
σ = √1.96 ≈ 2.49

Therefore, the answer is B) 2.49.

Question 12

Probability ranges between 0 and 1 and is never negative.

Accepted Answer

Probability is a measure of the likelihood of an event occurring, and it cannot have a negative value. Therefore, its range is between 0 and 1, inclusive of both endpoints.

Question 13

The sample space is equal to the total number of random outcomes possible for a random variable.

Accepted Answer

The sample space represents all possible outcomes of a random variable or experiment. It includes all the possible values that a random variable can take. Therefore, the size of the sample space equals the total number of possible outcomes for a random variable.

Question 14

If an outcome has a 1 in 100 chance of occurrence,then the probability of that outcome is p = .10.

Accepted Answer

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. 
In this case, the probability of occurrence is 1/100, which is equal to 0.01 or 1%. Therefore, the probability is p = 0.01, not p = 0.10.

Question 15

A probability can be stated as a proportion.

Accepted Answer

A probability is defined as the proportion of a desired outcome to the total number of possible outcomes. Therefore, it can be expressed as a proportion between 0 and 1, where 0 represents impossible and 1 represents certain.

Question 16

If the standard deviation of a probability distribution is 9,then the variance is
A)3
B)9
C)81
D)unknown

Accepted Answer

The variance is equal to the square of the standard deviation. Therefore, the variance is (9)^2 = 81.

Question 17

The probability of an outcome is particularly useful for predicting the likelihood of fixed events.

Accepted Answer

The probability of an outcome is useful for predicting the likelihood of random events, not fixed events. Fixed events have outcomes that are certain and do not involve chance.

Question 18

A distribution of probabilities for random outcomes of a bivariate or dichotomous random variable is called a
A)binomial probability distribution
B)distribution of expected values
C)random variable distribution
D)mathematical expectation

Accepted Answer

A distribution of probabilities for random outcomes of a bivariate or dichotomous random variable is referred to as a binomial probability distribution. The other options do not accurately describe this type of distribution.

Question 19

For mutually exclusive outcomes,one or the other outcome can occur (Outcome A or Outcome B),but not both outcomes (Outcome A and Outcome B)

Accepted Answer

This is the definition of mutually exclusive outcomes.

Question 20

Below is the probability distribution for random variable x.What is the standard deviation of this probability distribution? 
A)0.48
B)0.69
C)0.24
D)2.00

Accepted Answer

The answer of Below is the probability distribution for random...

Quiz 5: Probability, Normal Distributions, and Z Scores

A researcher determines that the probability of missing class among students at a local school is p = .16.Assuming that the school has 300 students enrolled,how many students can we expect to miss class on a given day? Hint: This is a binomial probability distribution.

A researcher reports that the probability of a college student living on campus is p = .38.If a small local college has 2,000 students enrolled,then what is the standard deviation of college students living on campus? Hint: This is a binomial probability distribution.

The probability of an outcome can be any positive value.

Each of the following is an example of a binomial distribution,except

A researcher determines that the relative frequency of participants with prescription glasses is .23.Hence,the probability that participants will wear prescription glasses must be greater than p = .23.

The relative frequency of an outcome is the probability of its occurrence.

Below is the probability distribution for the number of times students had to take the same exam before passing it.What is the value at the second standard deviation above the mean for this probability distribution?

If a complimentary outcome has a 1 in 10 chance of occurrence,then the probability of that outcome is p = .10.

If the variance of a probability distribution is 121,then the standard deviation is

Below is the probability distribution for random variable x.What is the standard deviation of this probability distribution?