Deck 5: Continuous Random Variables

Question 1

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and

A)0.02
B)0.2
C)0.3
D)0.16

Answer 1

B

Question 2

For a continuous probability distribution, the probability that x is between a and b is the same
regardless of whether or not you include the endpoints, a and b, of the interval.

Answer 2

True

Question 3

Suppose x is a uniform random variable with c = 10 and

A)0.6
B)0.4
C)0.1
D)0.9

Answer 3

B

Question 4

Suppose x is a uniform random variable with Round to the nearest hundredth when necessary.

A)0.5
B)0.8
C)1
D)0.2

Question 5

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 6.5 to 8.5 millimeters. Any ball bearing with a diameter of
Over 8.25 millimeters or under 6.75 millimeters is considered defective. What is the probability that
A randomly selected ball bearing is defective?

A).75
B).25
C).50
D)0

Question 6

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:

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

Question 7

Suppose x is a random variable best described by a uniform probability distribution with c = 20 and

A)0.5
B)1
C)0.2
D)0

Question 8

Suppose x is a random variable best described by a uniform probability distribution with c = 100 and

A)0.5
B)0
C)1
D)0.6

Question 9

The number of children in a family can be modelled using a continuous random variable.

Question 10

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 6.5 to 8.5 millimeters. What is the probability that a
Randomly selected ball bearing has a diameter greater than 7.4 millimeters?

A)3.5
B)0.8706
C)0.4933
D)0.55

Question 11

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and

A)0.2
B)0.02
C)0.16
D)0.8

Question 12

For any continuous probability distribution, P(x = c)= 0 for all values of c.

Question 13

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 60°F to 92°F. What is the probability that the high temperature on a day in August exceeds
65°F?

A)0.4276
B)0.0313
C)0.8438
D)0.1562

Question 14

Suppose x is a random variable best described by a uniform probability distribution with c = 30 and

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

Question 15

Question 16

Suppose x is a random variable best described by a uniform probability distribution with c = 2 and d = 6. Find the value of a that makes the following probability statement true:

A)3
B)0.8
C)4
D)4.5

Question 17

High temperatures in a certain city for the month of August follow a uniform distribution over the interval 78°F to 108°F. Find the temperature which is exceeded by the high temperatures on 90% of
The days in August.

A)108°F
B)105°F
C)88°F
D)81°F

Question 18

Suppose x is a random variable best described by a uniform probability distribution with c = 3 and d = 7. Find the value of a that makes the following probability statement true:

A)4
B)5.8
C)3
D)6

Question 19

Suppose x is a random variable best described by a uniform probability distribution with c = 20 and

A)0.4
B)0.5
C)0.04
D)0.08

Question 20

The total area under a probability distribution equals 1.

Question 21

The age of customers at a local hardware store follows a uniform distribution over the interval from 18 to 60 years old. Find the average age of customers to this hardware store.

A)45 years old
B)60 years old
C)39 years old
D)50 years old

Question 22

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.

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

Question 23

Use the standard normal distribution to find

A).4878
B).0122
C).8821
D).8944

Question 24

Which geometric shape is used to represent areas for a uniform distribution?

A)Triangle
B)Bell curve
C)Circle
D)Rectangle

Question 25

The age of customers at a local hardware store follows a uniform distribution over the interval from 18 to 60 years old. Find the probability that the next customer who walks through the door
Exceeds 50 years old. Round to the nearest ten-thousandth.

A)0.8333
B)0.2381
C)0.3600
D)0.7619

Question 26

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.

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

Question 27

A machine is set to pump cleanser into a process at the rate of 6 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 5.5 to 8.5 gallons per minute. What is the probability that at
The time the machine is checked it is pumping more than 7.0 gallons per minute?

A).50
B).667
C).7692
D).25

Question 28

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

Question 29

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 40 to 90. What is the mean outcome of this experiment?

A)90
B)40
C)65
D)70

Question 30

The diameters of ball bearings produced in a manufacturing process can be described using a uniform distribution over the interval 8.5 to 10.5 millimeters. What is the mean diameter of ball
Bearings produced in this manufacturing process?

A)9.5 millimeters
B)10.0 millimeters
C)9.0 millimeters
D)10.5 millimeters

Question 31

Use the standard normal distribution to find

A).0122
B).5122
C).6831
D).4878

Question 32

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 9.5 gallons per minute. Find the variance of the
Distribution.

A)5.33
B)0.08
C)0.33
D)24.08

Question 33

A machine is set to pump cleanser into a process at the rate of 4 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 3.5 to 4.5 gallons per minute. Find the
probability that the machine pumps less than 3.75 gallons during a randomly selected
minute.

Question 34

The diameters of ball bearings produced in a manufacturing process can be described
using a uniform distribution over the interval 4.5 to 9.5 millimeters. What is the probability
of a randomly selected ball bearing having a diameter less than 6.5 millimeters?

Question 35

Use the standard normal distribution to find

A).5122
B).7888
C).8817
D).4878

Question 36

Suppose x is a uniform random variable with c = 10 and d = 90. Find the mean of the
random variable x.

Question 37

Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 20 to 70. What is the probability that this experiment results in an outcome
Less than 30? Round to the nearest hundredth when necessary.

A)1
B)0.11
C)0.27
D)0.2

Question 38

High temperatures in a certain city for the month of August follow a uniform distribution
over the interval 75°F to 95°F. What is the probability that a random day in August has a
high temperature that exceeds 80°F?

Question 39

A machine is set to pump cleanser into a process at the rate of 10 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 10.0 to 13.0 gallons per minute. Would you expect the
Machine to pump more than 12.85 gallons per minute?

A)Yes, since .95 is a high probability.
B)No, since .95 is a high probability.
C)Yes, since .05 is a high probability.
D)No, since .05 is a low probability.

Question 40

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.

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

Question 41

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 ounces and a standard deviation of 0.30 ounce. Each can holds a
Maximum of 12.75 ounces of soda. Every can that has more than 12.75 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 probability that a randomly selected can will need to go through this process?

A).3413
B).6587
C).1587
D).8413

Question 42

Nearly 100% of the observed occurrences of a random variable x that is normally distributed will
fall within three standard deviations of the mean of the distribution of x.

Question 43

Which shape is used to represent areas for a normal distribution?

A)Rectangle
B)Bell curve
C)Circle
D)Triangle

Question 44

The volume of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.45 ounces and a standard deviation of 0.30 ounce. The company
Receives complaints from consumers who actually measure the amount of soda in the cans and
Claim that the volume is less than the advertised 12 ounces. What proportion of the soda cans
Contain less than the advertised 12 ounces of soda?

A).9332
B).5668
C).4332
D).0668

Question 45

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 440 seconds and a standard deviation of 60 seconds. Find the probability that a randomly
Selected boy in secondary school can run the mile in less than 302 seconds.

A).5107
B).9893
C).4893
D).0107

Question 46

For a standard normal random variable, find the probability that z exceeds the value -1.65.

A)0.9505
B)0.5495
C)0.4505
D)0.0495

Question 47

Question 48

Question 49

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. Between what times do we expect
Approximately 95% of the boys to run the mile?

A)between 377.75 and 542.28 seconds
B)between 365 and 555 seconds
C)between 362 and 558 seconds
D)between 0 and 542.28 seconds

Question 50

Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $500 per month and a standard deviation of $50 per
Month. Refer to such expenses as PCEʹs (personal call expenses). Using the distribution above,
What is the probability that during a randomly selected month PCEʹs were between $375.00 and
$590.00?

A).0421
B).0001
C).9999
D).9579

Question 51

The weight of corn chips dispensed into a 12-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 12.5 ounces and a standard deviation
Of 0.2 ounce. What proportion of the 12-ounce bags contain more than the advertised 12 ounces of
Chips?

A).0062
B).5062
C).4938
D).9938

Question 52

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.

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

Question 53

Question 54

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

Question 55

Use the standard normal distribution to find

A).9270
B).8822
C).5496
D).6167

Question 56

Question 57

Use the standard normal distribution to find

A).7888
B).9809
C).0198
D).0606

Question 58

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?

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

Question 59

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%?

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

Question 60

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.

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

Question 61

A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 5 milliliters (ml)
And a standard deviation of 0.4 ml. Answer the following questions based on this information.
What proportion of the paint cans contain less than 5.54 ml of the dye?

A)0.9115
B)0.5885
C)0.9885
D)0.0885

Question 62

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 8600 miles. If the
manufacturer guarantees the tread life of the tires for the first 49,680 miles, what
proportion of the tires will need to be replaced under warranty?

Question 63

Farmers often sell fruits and vegetables at roadside stands during the summer. One such
roadside stand has a daily demand for tomatoes that is approximately normally
distributed with a mean of 128 tomatoes and a standard deviation of 30 tomatoes. How
many tomatoes must be available on any given day so that there is only a 1.5% chance that
all tomatoes will be sold?

Question 64

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 1900 miles. What is the
Probability a certain tire of this brand will last between 56,010 miles and 56,580 miles?

A).0180
B).9813
C).4649
D).4920

Question 65

The rate of return for an investment can be described by a normal distribution with mean
40% and standard deviation 3%. What is the probability that the rate of return for the
investment exceeds 46%?

Question 66

The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. What proportion of the milk vendors had prices that were less than $3.075 per
Gallon?

A)0.3944
B)0.2112
C)0.8944
D)0.1056

Question 67

The board of examiners that administers the real estate brokerʹs examination in a certain
state found that the mean score on the test was 507 and the standard deviation was 72. If
the board wants to set the passing score so that only the best 10% of all applicants pass,
what is the passing score? Assume that the scores are normally distributed.

Question 68

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%?

Question 69

Question 70

Question 71

The preventable monthly loss at a company has a normal distribution with a mean of $5700 and a standard deviation of $30. A new policy was put into place, and the preventable loss the next
Month was $5520. What inference can you make about the new policy?

A)The new policy is probably less effective than the one it replaced.
B)Because the probability that the monthly loss would be as low as $5520 is not very small, the new policy is not working.
C)Because the probability that the monthly loss would be as low as $5520 is small, the new policy is working.
D)While the probability that the monthly loss would be as low as $5520 is small, it is not unexpected.

Question 72

The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. Find the price for which 12.3% of milk vendors exceeded.

A)$3.238
B)$3.316
C)$3.084
D)$3.215

Question 73

The board of examiners that administers the real estate brokerʹs examination in a certain
state found that the mean score on the test was 588 and the standard deviation was 72. If
the board wants to set the passing score so that only the best 80% of all applicants pass,
what is the passing score? Assume that the scores are normally distributed.

Question 74

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?

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

Question 75

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 2800 miles. What warranty
Should the company use if they want 96% of the tires to outlast the warranty?

A)64,900 miles
B)62,800 miles
C)55,100 miles
D)57,200 miles

Question 76

Question 77

Question 78

A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 5 milliliters (ml)
And a standard deviation of 0.4 ml. Answer the following questions based on this information.
Find the dye amount that represents the 9th percentile of the distribution.

A)4.964 ml
B)5.536 ml
C)4.836 ml
D)4.936 ml
E)4.464 ml

Question 79

Farmers often sell fruits and vegetables at roadside stands during the summer. One such
roadside stand has a daily demand for tomatoes that is approximately normally
distributed with a mean of 582 tomatoes and a standard deviation of 30 tomatoes. If there
are 540 tomatoes available to be sold at the roadside stand at the beginning of a day, what
is the probability that they will all be sold?

Question 80