Question 1

Assume Z is a standard normal random variable with P(-z < Z < z) = 0.8764.What is z?

Accepted Answer

A)   0.3764
B)   1.16
C)   1.54
D)   3.08 C

Question 2

The return on investment for a particular security has historically followed a normal distribution with a mean profit of 4.75% and standard deviation of 1.5%.If the historical pattern holds, what is the probability of investing in this security and seeing greater than a 6% return?

Accepted Answer

A)   0.7967
B)   0.8333
C)   0.2033
D)   0.1666 C

Question 3

Which of the following statements is true with regard to continuous random variables?

Accepted Answer

A)   The height of the curve shows the probability of an event.
B)   The probability of an event A occurring is always equal to one.
C)   Probabilities of events are determined from areas under the curve.
D)   The probability distribution is always mound-shaped. C

Question 4

Suppose the cumulative distribution function (CDF) of continuous random variable X is defined as follows:  where x ≥ 0.What is P(X > 1.25)?

Accepted Answer

A)   0.7467
B)   0.5833
C)   0.2533
D)   0.7333

Question 5

For any continuous random variable X, if both a and b are fixed real numbers such that a < b, then P(a ≤ X ≤ b) will always be:

Accepted Answer

A)   P(X 
B)   P(X ≤ b) .
C)   P(X ≤ b)  - P(X 
D)   Both A and B are correct.

Question 6

Large electrical generation companies use so-called peaking generators to carry additional load when demand for electrical power is particularly high.Running these generators at very low loads is bad for them for a number of reasons.A particular peaking generator carries an average load of 20 MW, with standard deviation of 4.23 MW.If this generator's low load threshold is 10 MW, what percentage of time is this generator being run at a low load condition?

Accepted Answer

A)   0.91%
B)   2.36%
C)   99.09%
D)   1%

Question 7

The descriptive statistics for the age differences (husband age - wife age) from a sample of 100 married couples are shown here.  Based on these statistics, do the data appear to be normally distributed?

Accepted Answer

A)   Yes, because the mean and the median are roughly the same.
B)   Yes, because the value of IQR/s is roughly 1.3.
C)   No, because the value of IQR/s is less than 1.3.
D)   No, because the mean and the median are the same.

Question 8

Heights of children entering kindergarten are normally distributed with a mean height of 103 cm and a standard deviation of 1.27 cm.Sixty-seven percent of the children entering kindergarten are taller than:

Accepted Answer

A)   103 cm.
B)   0.44 cm.
C)   103.56 cm.
D)   102.44 cm.

Question 9

A child psychologist believes that the results from a standardized behavior test fail to hold to the assumption of normality.She samples 250 results from the test to evaluate normality.The average value of the 250 samples is 105.25, with a standard deviation of 21.2.She finds that 30% of the scores are greater than 168.What conclusion should she draw based solely on this finding?

Accepted Answer

A)   The data could be normal because we expect 30% of the readings from this data set to be greater than 168.
B)   The data are most likely not normal because drastically fewer than 30% of the observations should be this high if the data set were normal.
C)   The data are most likely not normal because more than 30% of the observations should be this high if the data set were normal.
D)   The determination of normality cannot reliably be made from this information.

Question 10

A density curve is a:

Accepted Answer

A)   mathematical device that adjusts (equalizes)  probability across the range of data.
B)   smooth curve that visually displays the distribution of probability for a continuous random variable.
C)   visual display that shows the gradual transition of probability that is adjusted to equalize a data set.
D)   tool of descriptive statistics that displays only the region of a data set that has a high concentration of readings.

Question 11

Which of the following statements is true with regard to continuous random variables?

Accepted Answer

A)   They can assume values at all points on an interval with no breaks between possible values.
B)   They are defined at specific values.
C)   Their probability density functions are symmetric.
D)   Their probability density functions define the probability that the random variable X equals a specific value x.

Question 12

A sample of recorded dog barks is analyzed for decibel intensity.The mean intensity is 62.25 decibels, with a variance of 4.45.If this data set is normally distributed, we would expect approximately 95% of the barks to be within what range?

Accepted Answer

A)   (58.03, 66.47) 
B)   (60.16, 64.36) 
C)   (55.92, 66.47) 
D)   (53.35, 71.15)

Question 13

Most production model hybrid cars use a large battery as the core component of their power system.The battery lifetime of a particular hybrid are follows an exponential distribution with a mean lifetime of 8.62 years.What is the probability that one of these hybrid cars will have a battery that will last between 8 and 10 years?

Accepted Answer

A)   0.3953
B)   0.0819
C)   0.6047
D)   0.1160

Question 14

Seismologists have discovered a thermal disturbance in a remote location near the polar ice caps.Since the disturbance appears to occur randomly, they model the event using an exponential random variable X.If the mean time between occurrences is 52.25 hours, what is the probability that there will be at least 24 hours between occurrences?

Accepted Answer

A)   0.0190
B)   0.3683
C)   1.000
D)   0.6317

Question 15

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 C4 150 0 64.940 0.0825 1.010 62.722 65.679
Variable Maximum
C4 67.445
If this data set were normal, which value would most likely fall into the first quartile?

Accepted Answer

A)   63.93
B)   65.073
C)   64.366
D)   63.730

Question 16

The Minitab descriptive statistics display from a data set is shown here:

Using the IQR/s criteria, do these data appear to be normally distributed?

Accepted Answer

A)   Yes, the data appear to be normally distributed because IQR/s is very close to the standard normal value of 0.6.
B)   No, the data do not appear to be normally distributed because IQR/s is not very close to the standard normal value of 0.6.
C)   Yes, the data appear to be normally distributed because IQR/s is very close to the standard normal value of 1.3.
D)   No, the data do not appear to be normally distributed because IQR/s is not very close to the standard normal value of 1.3.

Question 17

If X is a normal random variable with mean μ, standard deviation 0.15, and P(X < 2.10) = 0.025, what is the value of μ?

Accepted Answer

A)   2.394
B)   2.104
C)   2.096
D)   1.806

Question 18

Let X = the time (in minutes) that a postal clerk spends with her customers.This time is known to have an exponential distribution with an average of 4 minutes.What is the parameter λ for this random variable?

Accepted Answer

A)   4
B)   2
C)   0.5
D)   0.25

Question 19

Any distribution whose mean value is equal to the median with first and third quartiles equidistant from them both is:

Accepted Answer

A)   always normal.
B)   always non-normal.
C)   always symmetric.
D)   always skewed.

Question 20

What differentiates the standard normal distribution (Z) from any other arbitrary normal distribution?

Accepted Answer

A)   The Z distribution has the least amount of variability of all normal distributions.
B)   The Z distribution is the only normal distribution with a fixed real mean value.
C)   The Z distribution has a mean value of 0 and a variance/standard deviation of 1.
D)   The Z distribution has a mean value and variance that is defined, which is uncommon for the normal distribution.

Exam 7: Continuous Probability Distributions

Assume Z is a standard normal random variable with P(-z < Z < z) = 0.8764.What is z?

The return on investment for a particular security has historically followed a normal distribution with a mean profit of 4.75% and standard deviation of 1.5%.If the historical pattern holds, what is the probability of investing in this security and seeing greater than a 6% return?

Which of the following statements is true with regard to continuous random variables?

Suppose the cumulative distribution function (CDF) of continuous random variable X is defined as follows: where x ≥ 0.What is P(X > 1.25) ?

For any continuous random variable X, if both a and b are fixed real numbers such that a < b, then P(a ≤ X ≤ b) will always be:

The descriptive statistics for the age differences (husband age - wife age) from a sample of 100 married couples are shown here. Based on these statistics, do the data appear to be normally distributed?

Heights of children entering kindergarten are normally distributed with a mean height of 103 cm and a standard deviation of 1.27 cm.Sixty-seven percent of the children entering kindergarten are taller than:

A density curve is a:

Which of the following statements is true with regard to continuous random variables?

A sample of recorded dog barks is analyzed for decibel intensity.The mean intensity is 62.25 decibels, with a variance of 4.45.If this data set is normally distributed, we would expect approximately 95% of the barks to be within what range?

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 C4 150 0 64.940 0.0825 1.010 62.722 65.679 Variable Maximum C4 67.445 If this data set were normal, which value would most likely fall into the first quartile?

The Minitab descriptive statistics display from a data set is shown here: Using the IQR/s criteria, do these data appear to be normally distributed?

If X is a normal random variable with mean μ, standard deviation 0.15, and P(X < 2.10) = 0.025, what is the value of μ?

Let X = the time (in minutes) that a postal clerk spends with her customers.This time is known to have an exponential distribution with an average of 4 minutes.What is the parameter λ for this random variable?

Any distribution whose mean value is equal to the median with first and third quartiles equidistant from them both is:

What differentiates the standard normal distribution (Z) from any other arbitrary normal distribution?