Question 1

The standardized normal quantile value O_i is the z value that gives an area of i/(n − 1) to its right under the normal curve.

Accepted Answer

The standardized normal quantile value O_i is the z value that gives an area of i/(n − 1) to its left under the normal curve.

Question 2

If the random variable, X, is normally distributed and has a mean of µ and a standard deviation σ, then the mean and standard deviation, respectively, of (X − µ)/σ are
A) μ and σ.
B)  and s.
C) 1 and 0.
D) 0 and 1.

Accepted Answer

This is part of the definition of a normal distribution where the mean is always 0 and the standard deviation is always 1.

Question 3

The first step to constructing a normal probability plot is to A) calculate O_i. B) compute area i/(n + 1). C) construct a box-and-whiskers plot. D) order the values in the data.

Accepted Answer

We need the values in order to compute the quantity of i/(n+1).

Question 4

The random variable x has a uniform distribution when x lies between the values of 4 and 10. When x = 10, what is the value of f(x)?
A) 0
B) 1
C) 1/6
D) 1/14

Accepted Answer

For a continuous random variable, probability at a single value = 0.

Question 5

The grade a student received on an examination was transformed to a z value, which was negative. Therefore, we know that the student scored
A) higher than 16 percent of the class.
B) higher than 45 percent of the class.
C) above the first quartile.
D) below the mean.
E) lower than 16 percent of the class.

Accepted Answer

The mean is 0, so if the z value is negative, the student is to the left of the mean and therefore below or less than the mean.

Question 6

The price-to-earnings ratio for firms in a given industry is distributed according to the normal distribution. In this industry, a firm with a standard normal variable value of z = 1
A) has an above average price-to-earnings ratio.
B) has a below average price-to-earnings ratio.
C) has an average price-to-earnings ratio.
D) may have an above average or below average price-to-earnings ratio depending on the value of the mean.

Accepted Answer

This is due to the fact that a normal distribution has a mean of 0.

Question 7

If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour
A) is greater than the proportion earning less than $13 per hour.
B) is greater than the proportion earning less than $18 per hour.
C) is less than 50 percent.
D) is less than the proportion earning more than the mean wage.

Accepted Answer

Since the average is $15 and you are concerned with those making more than $13 an hour, $13 would be to the left of $15 on the graph. There would a higher proportion of those to the right of $13 than the left because most of the data would be centered around $15 since that is the average.

Question 8

The normal approximation of the binomial distribution is appropriate when
A) np ≥ 5.
B) n(1 − p) ≥ 5.
C) np ≤ 5.
D) n(1 − p) ≤ 5 and np ≤ 5.
E) np ≥ 5 and n(1 − p) ≥ 5.

Accepted Answer

If p is close to 0 or 1, then n needs to be even larger.

Question 9

Which of the following is a continuous distribution?
A) Poisson
B) hypergeometric
C) exponential
D) binomial

Accepted Answer

All of the other choices are discrete random variables.

Question 10

Values of the standard normal random variable are measured
A) with reference to specific units.
B) in the units in which the mean is measured.
C) in the number of standard deviations from the mean.
D) in squared units in which the mean is measured.
E) None of these answers are correct.

Accepted Answer

This number is given by the z table.

Question 11

The area under the normal curve between z = 0 and z = 1 is ________ the area under the normal curve between z = 1 and z = 2.
A) less than
B) greater than
C) equal to
D) less than, greater than, or equal to, depending on the value of the mean,
E) less than, greater than, or equal to, depending on the value of the standard deviation,

Accepted Answer

The normal curve centers around the mean of zero, and more data is concentrated close to the mean than further out by the tails.

Question 12

A study shows that employees who begin their workday at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is
A) 40 percent.
B) 20 percent.
C) 10 percent.
D) 30 percent.
E) 16.7 percent.

Accepted Answer

P(9:00 < x <9:10) = 10 min/50 min = 1/5 = 20%

Question 13

A property of continuous distributions is that
A) as with discrete random variables, the probability distribution can be approximated by a smooth curve.
B) probabilities for continuous variables can be approximated using discrete random variables.
C) unlike discrete random variables, probabilities can be found using tables.
D) unlike discrete random variables, the probability that a continuous random variable equals a specific value is zero [P(X = x) = 0].

Accepted Answer

This is due to the fact that there is an infinite amount of values that the continuous distribution could take on and, therefore, picking exactly one value is highly unlikely, or equal to zero.

Question 14

It is appropriate to use the uniform distribution to describe a continuous random variable x when
A) the area under the probability curve = 1.
B) the probability curve f(x) > 0.
C) the shape of the histogram of all possible values of x is nonsymmetrical.
D) relative frequencies of all possible values of x are about the same.

Accepted Answer

They all have about the same chance of occurring.

Question 15

In order to approximate the binomial distribution using the normal distribution, the following condition(s) must be met if p is near 1.
A) np > 5 only
B) n must be larger than just meeting the condition of np > 5.
C) n can be as small as np > 5.
D) n > 5

Accepted Answer

This is because as n gets closer and p gets closer to 0.5, the graph of a binomial distribution tends to have the symmetrical, bell shaped appearance of a normal curve.

Question 16

The relationship between the standard normal random variable, z, and normal random variable, X, is that
A) only the normal random variable X is continuous.
B) only the standard normal variable z is continuous.
C) the standard normal variable z counts the number of standard deviations that the value of the normal random variable X is away from its mean.
D) the values of the standard normal random variable z cannot be negative.
E) the values of the normal random variable X cannot be negative.

Accepted Answer

The standard normal variable is then organized into a z table.

Question 17

The ________ is a graphic that is used to visually check whether data come from a normal population.
A) exponential plot
B) normal probability plot
C) box-and-whiskers plot
D) normal distribution graph

Accepted Answer

We plot the ordered data against the corresponding standardized normal quartile values.

Question 18

The mean life of a pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months?
A) 500,073
B) 808,573
C) 191,537
D) 308,537

Accepted Answer

P(x < 36) = P(z < (36 − 40)/8) = P(z < −.5)
The area under the curve is .308537 × 1,000,000.

Question 19

A standard normal distribution has a mean of ________ and standard deviation of ________.
A) zero, zero
B) zero, one
C) one, one
D) one, zero

Accepted Answer

This is part of the definition of the standard normal distribution.

Question 20

The ________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.
A) normal
B) exponential
C) Poisson
D) binomial
E) uniform

Accepted Answer

This is a Poisson distribution where we are not looking for the number of successes or failures, but the time between those successes or failures.

Quiz 7: Continuous Random Variables

The standardized normal quantile value O_i is the z value that gives an area of i/(n − 1) to its right under the normal curve.

If the random variable, X, is normally distributed and has a mean of µ and a standard deviation σ, then the mean and standard deviation, respectively, of (X − µ) /σ are

The first step to constructing a normal probability plot is to

The random variable x has a uniform distribution when x lies between the values of 4 and 10. When x = 10, what is the value of f(x) ?

The grade a student received on an examination was transformed to a z value, which was negative. Therefore, we know that the student scored

The price-to-earnings ratio for firms in a given industry is distributed according to the normal distribution. In this industry, a firm with a standard normal variable value of z = 1

If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour

The normal approximation of the binomial distribution is appropriate when

Which of the following is a continuous distribution?

Values of the standard normal random variable are measured

The area under the normal curve between z = 0 and z = 1 is ________ the area under the normal curve between z = 1 and z = 2.

A study shows that employees who begin their workday at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is

A property of continuous distributions is that

It is appropriate to use the uniform distribution to describe a continuous random variable x when

In order to approximate the binomial distribution using the normal distribution, the following condition(s) must be met if p is near 1.

The relationship between the standard normal random variable, z, and normal random variable, X, is that

The ________ is a graphic that is used to visually check whether data come from a normal population.

The mean life of a pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months?

A standard normal distribution has a mean of and standard deviation of .

The ________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.

Quiz 7: Continuous Random Variables

The standardized normal quantile value Oi is the z value that gives an area of i/(n − 1) to its right under the normal curve.

If the random variable, X, is normally distributed and has a mean of µ and a standard deviation σ, then the mean and standard deviation, respectively, of (X − µ) /σ are

The first step to constructing a normal probability plot is to

The random variable x has a uniform distribution when x lies between the values of 4 and 10. When x = 10, what is the value of f(x) ?

The grade a student received on an examination was transformed to a z value, which was negative. Therefore, we know that the student scored

The price-to-earnings ratio for firms in a given industry is distributed according to the normal distribution. In this industry, a firm with a standard normal variable value of z = 1

If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour

The normal approximation of the binomial distribution is appropriate when

Which of the following is a continuous distribution?

Values of the standard normal random variable are measured

The area under the normal curve between z = 0 and z = 1 is ________ the area under the normal curve between z = 1 and z = 2.

A study shows that employees who begin their workday at 9:00 a.m. vary their times of arrival uniformly from 8:40 a.m. to 9:30 a.m. The probability that a randomly chosen employee reports to work between 9:00 and 9:10 is

A property of continuous distributions is that

It is appropriate to use the uniform distribution to describe a continuous random variable x when

In order to approximate the binomial distribution using the normal distribution, the following condition(s) must be met if p is near 1.

The relationship between the standard normal random variable, z, and normal random variable, X, is that

The ________ is a graphic that is used to visually check whether data come from a normal population.

The mean life of a pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months?

A standard normal distribution has a mean of ________ and standard deviation of ________.

The ________ distribution would most likely be used to describe the distribution of time between arrivals of customers at the grocery store.

The standardized normal quantile value O_i is the z value that gives an area of i/(n − 1) to its right under the normal curve.

A standard normal distribution has a mean of and standard deviation of .