Question 1

If the random variable X has a mean of µ and a standard deviation σ,then (X - µ)/σ has a mean and standard deviation respectively:
A)μ and σ
B) 
C)1 and 0
D)0 and 1

Accepted Answer

(X - µ)/σ is a standardized variable with mean 0 and standard deviation 1, also known as a z-score. This is a fundamental concept in statistics and is used in many statistical calculations and analyses.

Question 2

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

The normal approximation of the binomial distribution is appropriate when both np ≥ 5 and n(1-p) ≥ 5. This is because the normal distribution is a continuous distribution and assumes a large enough sample size for accuracy. If either np or n(1-p) is less than 5, the binomial distribution is too skewed to approximate with a normal distribution. Therefore, the best choice is E, which satisfies both conditions.

Question 3

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 mean wage is $15 per hour, the proportion of workers earning more than $15 per hour is 50%. Therefore, the proportion of workers earning less than $13 per hour is less than 50%, and the proportion of workers earning more than $13 per hour must be greater than 50%.

Question 4

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.

Accepted Answer

Values of the standard normal random variable are measured in the number of standard deviations from the mean. This is because the standard normal distribution has a mean of 0 and a standard deviation of 1, so each value represents how many standard deviations a particular value is from the mean.

Question 5

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)A,B,or C above,depending on the value of the mean
E)A,B,or C above,depending on the value of the standard deviation

Accepted Answer

The normal distribution is symmetric around the mean, and the area between z = 0 and z = 1 is greater than the area between z = 1 and z = 2 because the curve is higher and more concentrated around the mean.

Question 6

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)500,000
B)808,500
C)191,500
D)308,500

Accepted Answer

The answer of The mean life of a pair of...

Question 7

A study shows that employees that 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

The answer of A study shows that employees that begin...

Question 8

The first step to constructing a normal probability plot is: 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

The first step in constructing a normal probability plot is to order the values in the data from smallest to largest.

Question 9

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

A negative z-score indicates that the student's score was below the mean of the class.

Question 10

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

The uniform distribution is used to describe a continuous random variable when the relative frequencies of all possible values of x are about the same. The other options do not necessarily apply to the uniform distribution. The area under the probability curve is always equal to 1 for any probability distribution, not just the uniform distribution. The probability curve can have values that are equal to zero for certain x values in the uniform distribution, and the shape of the histogram can be either symmetrical or nonsymmetrical for the uniform distribution.

Question 11

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 12

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.

Accepted Answer

Since z=1 is one standard deviation above the mean in a normal distribution, the firm with z=1 has an above average price-to-earnings ratio.

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 property is known as the continuity property and is a fundamental characteristic of continuous distributions. It means that the probability of a continuous random variable taking a specific value is zero, as there are infinitely many possible values that the variable could take. Instead, we can only talk about the probability of the variable falling within a range of values.

Question 14

Which of the following is a continuous distribution?
A)Poisson
B)Hypergeometric
C)Exponential
D)Binomial

Accepted Answer

A continuous distribution is one where the random variable can take on any value within a range. The Poisson, Hypergeometric, and Binomial distributions are all discrete as they deal with a count of events or successes. The Exponential distribution, however, is continuous as it models the time between events occurring which can take on any positive value.

Question 15

The ___________ is a graphic that is used to check visually 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

The normal probability plot is specifically designed to check whether data come from a normal population. It plots the observed data against the expected data values from a normal distribution. If the points on the plot fall roughly along a straight line, then the data can be considered approximately normally distributed. The other options listed (exponential plot, box and whisker plot, normal distribution graph) may be useful for visualizing data in other ways, but they are not designed to check for normality specifically.

Question 16

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

A standard normal distribution has a mean of zero and a standard deviation of one. This means that the data is centered around zero and the units of measurement are in terms of standard deviations from the mean.

Question 17

The standardized normal quartile 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 quartile value O_i is not a standard notation for a z-score. It is unclear what i and n represent in this context. Therefore, the statement is not meaningful.

Question 18

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 relationship between the standard normal random variable z and normal random variable X is that 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. This means that the standard normal random variable z is a scaled version of the normal random variable X, with a mean of 0 and a standard deviation of 1.

Question 19

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 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

The exponential distribution is commonly used to model the time between arrivals of events, such as customers arriving at a store. The Poisson distribution could also be used, but it is typically used to model the number of events occurring in a fixed time period, rather than the time between events. The other distributions listed are not appropriate for this scenario.

Quiz 6: Continuous Random Variables

If the random variable X has a mean of µ and a standard deviation σ,then (X - µ) /σ has a mean and standard deviation respectively:

The normal approximation of the binomial distribution is appropriate when:

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:

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.

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 study shows that employees that 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:

The first step to constructing a normal probability plot is:

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

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 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 property of continuous distributions is that:

Which of the following is a continuous distribution?

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

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

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

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

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

Quiz 6: Continuous Random Variables

If the random variable X has a mean of µ and a standard deviation σ,then (X - µ) /σ has a mean and standard deviation respectively:

The normal approximation of the binomial distribution is appropriate when:

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:

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.

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 study shows that employees that 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:

The first step to constructing a normal probability plot is:

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

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 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 property of continuous distributions is that:

Which of the following is a continuous distribution?

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

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

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

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

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

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

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