Data Analysis Statitics

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Question 1 (3 points)

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Which of the following is the operation called standardizing?

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Question 2 (3 points)

Given that Z is a standard normal random variable, P(-1.0 Z 1.5) is

Question 2 options:

	0.8413
	0.7745
	0.0919
	0.9332

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Question 3 (3 points)

is the:

Question 3 options:

	rule of complements
	commutative rule
	addition rule
	rule of opposites

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Question 4 (3 points)

Which of following statements are true regarding the probability distribution of a random variable X?

Question 4 options:

	The probabilities must be nonnegative
	The probabilities must sum to 1
	The random variable must be continuous
	Both (a) and (b)

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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:

	exhaustive
	independent
	mutually exclusive
	complementary

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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:

	.33
	.67
	.65
	.35

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Question 7 (3 points)

There are two types of random variables, they are

Question 7 options:

	complementary and cumulative
	discrete and continuous
	real and unreal
	exhaustive and mutually exclusive

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Question 8 (3 points)

If P(A) = 0.25 and P(B) = 0.65, then P(A and B) is:

Question 8 options:

	0.25
	0.40
	0.90
	Cannot be determined from the information given.

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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)

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

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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 relative likelihood
	measure of variability of the distribution
	measure of central location
	measure of skewness of the distribution

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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)

A continuous probability distribution is characterized by:

Question 14 options:

	counts
	a list of possible values
	a continuum of possible values
	an array of individual values

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Question 15 (5 points)

Consider a random variable X with the following probability distribution: Find the mean and the variance of X.

Question 15 options:

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Question 16 (3 points)

The president of a bank is attempting to arrange a meeting with the three vice presidents for a Friday weekly meeting. He believes that each of these three busy individuals, independently of the others, has about 40% chance of being able to attend the meeting. The probability distribution of X; the number of vice presidents who can attend the meeting is as follows: What is the probability that at least two of the three vice presidents can attend the meeting?

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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 is a male student?

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Question 18 (4 points)

The grades on the final examination given in a large organic chemistry class are normally distributed with a mean of 72 and a standard deviation of 8. The instructor of this class wants to assign an “A” grade to the top 10% of the scores, a “B” grade to the next 10% of the scores, a “C” grade to the next 10% of the scores, a “D” grade to the next 10% of the scores, and an “F” grade to all scores below the 60th percentile of this distribution. For a letter grade of B, find the lowest acceptable score within the established range. Provide your answer in the format XX.X, for example 83.4.

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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 less than two 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 exactly $28 at this store?

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Question 21 (3 points)

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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:

	13
	10
	30
	90

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Question 23 (2 points)

Two events A and B are said to be independent if P(A and B) = P(A) + P(B)

Question 23 options:

	True
	False

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Question 24 (2 points)

Conditional probability is the probability that an event will occur, with no other events taken into consideration.

Question 24 options:

	True
	False

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Question 25 (2 points)

Two or more events are said to be exhaustive if one of them must occur.

Question 25 options:

	True
	False

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Question 26 (2 points)

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

Question 26 options:

	True
	False

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Question 27 (2 points)

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

Question 27 options:

	True
	False

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Question 28 (2 points)

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

Question 28 options:

	True
	False

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Question 29 (2 points)

If Z is a standard normal variable, then P(Z > 1.50) = 0.9332

Question 29 options:

	True
	False

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Question 30 (2 points)

The normal distribution is the cornerstone of statistical theory. It is a continuous distribution and is characterized by a symmetric, bell-shaped curve.

Question 30 options:

	True
	False

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Question 31 (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 31 options:

	True
	False

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Question 32 (3 points)

Suppose that a marketing firm sends questionnaires to two different companies. Based on istorical evidence, the marketing research firm believes that each company, independently of the other, will return the questionnaire with a probability of 0.30. What is the probability that both questionnaires will be returned?

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Question 33 (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. If a dieter is selected at random, what is the probability that the dieter lost at most 7.5 pounds?

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