Question 1 (3 points)

The standard normal distribution has a mean of a standard deviation respectively equal to

Question 1 options:

1 and 1

0 and 0

1 and 0

0 and 1

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Question 2 (3 points)

Given that Z is a standard normal variable, the value z for which P(Z z) = 0.2580 is

Question 2 options:

0.242

-0.65

0.70

0.758

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Question 3 (3 points)

The result of tossing a coin once will be either head or tail. Let A and B be the events of observing head and tail, respectively. The events A and B are:

Question 3 options:

conditional

mutually exclusive

unilateral

independent

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Question 4 (3 points)

Which of the following statements are true?

Question 4 options:

Probabilities must be nonnegative.

Probabilities can either be positive or negative.

Probabilities can be any positive value.

Probabilities must be negative.

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Question 5 (3 points)

If P(A) = P(A|B), then events A and B are said to be

Question 5 options:

mutually exclusive

complementary

independent

exhaustive

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Question 6 (3 points)

The joint probabilities shown in a table with two rows, A1and A2 and two columns, B1 and B2, are as follows: P(A1 and B1) = .10, P(A1 and B2) = .30, P(A2 and B1) = .05, and P(A2 and B2) = .55. Then P(A1|B1), calculated up to two decimals, is

Question 6 options:

.65

.67

.33

.35

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Question 7 (3 points)

There are two types of random variables, they are

Question 7 options:

discrete and continuous

exhaustive and mutually exclusive

complementary and cumulative

real and unreal

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Question 8 (3 points)

If A and B are any two events with P(A) = .8 and P(B| ) = .7, then P( and B) is

Question 8 options:

.56

.14

.24

None of the above

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Question 9 (3 points)

Which of the following best describes the concept of marginal probability?

Question 9 options:

It is a measure of the likelihood that a particular event will occur, regardless of whether another event occurs.

It is a measure of the likelihood that a particular event will occur, given that another event has already occurred.

It is a measure of the likelihood of the simultaneous occurrence of two or more events.

None of the above.

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Question 10 (3 points)

We assume that the outcomes of successive trials in a binomial experiment are:

Question 10 options:

identical from trial to trial

probabilistically independent

probabilistically dependent

random number between 0 and 1

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Question 11 (3 points)

The mean of a binomial distribution with parameters n and p is given by:

Question 11 options:

np

n – p

n + p

n/p

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Question 12 (3 points)

The mean of a probability distribution is a:

Question 12 options:

measure of skewness of the distribution

measure of variability of the distribution

measure of relative likelihood

measure of central location

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Question 13 (3 points)

If the value of the standard normal random variable Z is positive, then the original score is where in relationship to the mean?

Question 13 options:

equal to the mean

to the left of the mean

to the right of the mean

None of the above

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Question 14 (3 points)

The standard deviation of a probability distribution must be:

Question 14 options:

a nonnegative number

a negative number

a number between 0 and 1

All of the above

None of the above

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Question 15 (5 points)

Consider a random variable X with the following probability distribution:

P(X=0) = 0.25, P(X=1) = 0.35, P(X=2) = 0.15, P(X=3) = 0.10, and P(X=4) = 0.15.

Find the mean and standard deviation of X.

Question 15 options:

Mean = 1.5500

Standard deviation = 1.3592

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Question 16 (3 points)

Consider a random variable X with the following probability distribution:

P(X=0) = 0.08, P(X=1) = 0.22, P(X=2) = 0.25, P(X=3) = 0.25, P(X=4) = 0.15, P(X=5) = 0.05

Find P(2<X<4)

Question 16 options:

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Question 17 (3 points)

Suppose that 20% of the students of Big Rapids High School play sports. Moreover, assume that 55% of all students are female, and 15% of all female students play sports.

If we choose a student at random from this school, what is the probability that this student is a female who does not play sports?

Question 17 options:

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Question 18 (4 points)

Scores on a mathematics examination appear to follow a normal distribution with mean of 65 and standard deviation of 15. The instructor wishes to give a grade of “C” to students scoring between the 60th and 70th percentiles on the exam. For what range of scores should a “C” grade be given?

Question 18 options:

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Question 19 (4 points)

The service manager for a new appliances store reviewed sales records of the past 20 sales of new microwaves to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new microwaves needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new microwaves sold.

What is the probability that only one of the 20 new microwaves sold will require a warranty repair in the first 90 days?

Question 19 options:

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Question 20 (3 points)

A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9.

What is the probability that a randomly selected customer will spend $20 or more at this store?

Question 20 options:

Question 21 (3 points)

A popular retail store knows that the distribution of purchase amounts by its customers is approximately normal with a mean of $30 and a standard deviation of $9.

What is the probability that a randomly selected customer will spend exactly $28 at this store?

Question 21 options:

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Question 22 (3 points)

If X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to

Question 22 options:

10

30

90

13

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Question 23 (2 points)

Suppose A and B are mutually exclusive events where P(A) = 0.2 and P(B) = 0.5, then P(A or B) = 0.70.

Question 23 options:

True

False

Question 24 (2 points)

If A and B are two independent events with P(A) = 0.20 and P(B) = 0.60, then P(A and B) = 0.80

Question 24 options:

True

False

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Question 25 (2 points)

The number of homeless people in Boston is an example of a discrete random variable.

Question 25 options:

True

False

Question 26 (2 points)

The multiplication rule for two events A and B is: P(A and B) = P(A|B)P(A).

Question 26 options:

True

False

Question 27 (2 points)

If events A and B have nonzero probabilities, then they can be both independent and mutually exclusive.

Question 27 options:

True

False

Question 28 (2 points)

Probability is a number between 0 and 1, inclusive, which measures the likelihood that some event will occur.

Question 28 options:

True

False

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Question 29 (2 points)

The left half under the normal curve is slightly smaller than the right half.

Question 29 options:

True

False

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Question 30 (2 points)

If X is a binomial random variable with n = 20, and p = 0.30, then P(X = 10) = 0.50.

Question 30 options:

True

False

Question 31 (2 points)

The binomial random variable represents the number of successes that occur in a specific period of time.

Question 31 options:

True

False

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Question 32 (2 points)

Using the standard normal curve, the Z- score representing the 99th percentile is 2.326.

Question 32 options:

True

False

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Question 33 (2 points)

Using the standard normal curve, the Z- score representing the 75th percentile is 0.674.

Question 33 options:

True

False

Question 34 (2 points)

A random variable X is normally distributed with a mean of 175 and a standard deviation of 50. Given that X = 150, its corresponding Z- score is –0.50.

Question 34 options:

True

False

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Question 35 (3 points)

In a particular community, there are medical doctors in 40% of the households. If a household is chosen at random from this community, what is the probability that there is not a medical doctor in this household?

Question 35 options:

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Question 36 (3 points)

Researchers studying the effects of a new diet found that the weight loss over a one-month period by those on the diet was normally distributed with a mean of 9 pounds and a standard deviation of 3 pounds.

What proportion of the dieters lost more than 12 pounds?