Question 1

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and $d = 50 . \text { Find } P ( 30 \leq x \leq 34 )$

Accepted Answer

A) 0.02 
B) 0.04 
C) 0.3 
D) 0.2

Question 2

If a data set is normally distributed, what is the proportion of measurements you would expect to fall within $\mu \pm \sigma$ ?

Accepted Answer

A)  $95 \%$ 
B)  $100 \%$ 
C)  $50 \%$ 
D)  $68 \%$

Question 3

After a particular heavy snowstorm, the depth of snow reported in a mountain village followed a uniform distribution over the interval from 15 to 22 inches of snow. Find the probability that a
Randomly selected location in this village had between 17 and 18 inches of snow. Round to the
Nearest ten-thousandth.

Accepted Answer

A) 0.4286 
B) 0.2857 
C) 0.5714 
D) 0.1429

Question 4

Suppose x is a random variable best described by a uniform probability distribution with c = 2 and d = 4. Find the value of a that makes the following probability statement true: $\mathrm { P } ( \mathrm { x } \geq \mathrm { a } ) = 0.75$

Accepted Answer

A) 2.5 
B) 2.9 
C) 1.5 
D) 3.5

Question 5

You are performing a study about the weight of preschoolers. A previous study found the
weights to be normally distributed with a mean of 30 pounds and a standard deviation of
4 pounds. You randomly sample 30 preschool children and find their weights (in pounds)
to be as follows. $$\begin{array} { l l l l l l l l l l } 
25 & 25 & 26 & 26.5 & 27 & 27 & 27.5 & 28 & 28 & 28.5 \
29 & 29 & 30 & 30 & 30.5 & 31 & 31 & 32 & 32.5 & 32.5 \
33 & 33 & 34 & 34.5 & 35 & 35 & 37 & 37 & 38 & 38
\end{array}$$ Draw a histogram to display the data. Is it reasonable to assume that the weights are
normally distributed? Why?

Accepted Answer

The answer of You are performing a study about the...

Question 6

Data has been collected and a normal probability plot for one of the variables is shown below. Based on your knowledge of normal probability plots, do you believe the variable in question is
Normally distributed? The data are represented by theʺoʺ symbols in the plot.

Accepted Answer

A)  Yes. The plot reveals a straight line and this indicates the variable is normally distributed. 
B)  Yes. The plot reveals a curve and this indicates the variable is normally distributed. 
C)  No. The plot does not reveal a straight line and this indicates the variable is not normally distributed.

Question 7

Suppose that the random variable $x$ has an exponential distribution with $\theta = 1.5$. Find the probability that $x$ will assume a value within the interval $\mu \pm 2 \sigma$.

Accepted Answer

A)  864665 
B)  $.950213$ 
C)  049787 
D)  .716531

Question 8

A machine is set to pump cleanser into a process at the rate of 8 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the
Uniform distribution over the interval 7.5 to 10.5 gallons per minute. Find the probability that
Between 8.0 gallons and 9.0 gallons are pumped during a randomly selected minute.

Accepted Answer

A) 0.33 
B) 0.67 
C) 1 
D) 0

Question 9

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a
Mean of 460 seconds and a standard deviation of 50 seconds. The fitness association wants to
Recognize the fastest 10% of the boys with certificates of recognition. What time would the boys
Need to beat in order to earn a certificate of recognition from the fitness association?

Accepted Answer

A) 377.75 seconds 
B) 396 seconds 
C) 524 seconds 
D) 542.25 seconds

Question 10

Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $700 per month and a standard deviation of $50 per
Month. Refer to such expenses as PCEʹs (personal call expenses). Find the probability that a
Randomly selected month had PCEʹs below $550.

Accepted Answer

A) 0.7857 
B) 0.2143 
C) 0.9987 
D) 0.0013

Question 11

Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $900 per month and a standard deviation of $50 per
Month. Refer to such expenses as PCEʹs (personal call expenses). Find the point in the distribution
Below which 2.5% of the PCEʹs fell.

Accepted Answer

A) $802.00 
B) $22.50 
C) $877.50 
D) $998.00

Question 12

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2100 miles. What is the
Probability a particular tire of this brand will last longer than 57,900 miles?

Accepted Answer

A) .2266 
B) .1587 
C) .8413 
D) .7266

Question 13

After a particular heavy snowstorm, the depth of snow reported in a mountain village followed a uniform distribution over the interval from 15 to 22 inches of snow. Find the standard deviation of
The snowfall amounts.

Accepted Answer

A) 18.5 inches 
B) 1.42 inches 
C) 2.02 inches 
D) 4.08 inches

Question 14

The mean of the standard normal distribution is 1 and the standard deviation is 0.

Accepted Answer

A) True 
 B)False

Question 15

The time (in years)until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5
Years or more.

Accepted Answer

A) 0.770210 
B) 0.229790 
C) 0.506617 
D) 0.493383

Question 16

Suppose x is a uniform random variable with c = 20 and d = 80. Find the standard deviation of x.

Accepted Answer

A)  $\sigma = 2.24$ 
B)  $\sigma = 17.32$ 
C)  $\sigma = 28.87$ 
D)  $\sigma = 2.89$

Question 17

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a standard deviation of 0.20 ounce. Every can that has more than 12.50 ounces of
Soda poured into it causes a spill and the can must go through a special cleaning process before it
Can be sold. What is the mean amount of soda the machine should dispense if the company wants
To limit the percentage that must be cleaned because of spillage to 3%?

Accepted Answer

A) 12.8760 ounces 
B) 12.0660 ounces 
C) 12.9340 ounces 
D) 12.1240 ounces

Question 18

The rate of return for an investment can be described by a normal distribution with mean
42% and standard deviation 3%. What is the probability that the rate of return for the
investment will be at least 37.5%?

Accepted Answer

The answer of The rate of return for an investment...

Exam 5: Continuous Random Variables

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and $d = 50 . \text { Find } P ( 30 \leq x \leq 34 )$

If a data set is normally distributed, what is the proportion of measurements you would expect to fall within $\mu \pm \sigma$ ?

Suppose x is a random variable best described by a uniform probability distribution with c = 2 and d = 4. Find the value of a that makes the following probability statement true: $\mathrm { P } ( \mathrm { x } \geq \mathrm { a } ) = 0.75$

Data has been collected and a normal probability plot for one of the variables is shown below. Based on your knowledge of normal probability plots, do you believe the variable in question is Normally distributed? The data are represented by theʺoʺ symbols in the plot.

Suppose that the random variable $x$ has an exponential distribution with $\theta = 1.5$ . Find the probability that $x$ will assume a value within the interval $\mu \pm 2 \sigma$ .

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2100 miles. What is the Probability a particular tire of this brand will last longer than 57,900 miles?

After a particular heavy snowstorm, the depth of snow reported in a mountain village followed a uniform distribution over the interval from 15 to 22 inches of snow. Find the standard deviation of The snowfall amounts.

The mean of the standard normal distribution is 1 and the standard deviation is 0.

The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5 Years or more.

Suppose x is a uniform random variable with c = 20 and d = 80. Find the standard deviation of x.

The rate of return for an investment can be described by a normal distribution with mean 42% and standard deviation 3%. What is the probability that the rate of return for the investment will be at least 37.5%?

Exam 5: Continuous Random Variables

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and d=50. Find P(30≤x≤34) d = 50 . \text { Find } P ( 30 \leq x \leq 34 ) d=50. Find P(30≤x≤34)

If a data set is normally distributed, what is the proportion of measurements you would expect to fall within μ±σ\mu \pm \sigmaμ±σ ?

Suppose x is a random variable best described by a uniform probability distribution with c = 2 and d = 4. Find the value of a that makes the following probability statement true: P(x≥a) =0.75\mathrm { P } ( \mathrm { x } \geq \mathrm { a } ) = 0.75P(x≥a) =0.75

Data has been collected and a normal probability plot for one of the variables is shown below. Based on your knowledge of normal probability plots, do you believe the variable in question is Normally distributed? The data are represented by theʺoʺ symbols in the plot.

Suppose that the random variable xxx has an exponential distribution with θ=1.5\theta = 1.5θ=1.5 . Find the probability that xxx will assume a value within the interval μ±2σ\mu \pm 2 \sigmaμ±2σ .

The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2100 miles. What is the Probability a particular tire of this brand will last longer than 57,900 miles?

After a particular heavy snowstorm, the depth of snow reported in a mountain village followed a uniform distribution over the interval from 15 to 22 inches of snow. Find the standard deviation of The snowfall amounts.

The mean of the standard normal distribution is 1 and the standard deviation is 0.

The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5 Years or more.

Suppose x is a uniform random variable with c = 20 and d = 80. Find the standard deviation of x.

The rate of return for an investment can be described by a normal distribution with mean 42% and standard deviation 3%. What is the probability that the rate of return for the investment will be at least 37.5%?

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and $d = 50 . \text { Find } P ( 30 \leq x \leq 34 )$

If a data set is normally distributed, what is the proportion of measurements you would expect to fall within $\mu \pm \sigma$ ?

Suppose x is a random variable best described by a uniform probability distribution with c = 2 and d = 4. Find the value of a that makes the following probability statement true: $\mathrm { P } ( \mathrm { x } \geq \mathrm { a } ) = 0.75$

Suppose that the random variable $x$ has an exponential distribution with $\theta = 1.5$ . Find the probability that $x$ will assume a value within the interval $\mu \pm 2 \sigma$ .