Devry MATH221 Week 4 Homework Latest 2019 JULY Question # 00603453 Course Code : MATH221 Subject: Mathematics Due on: 08/05/2019 Posted On: 08/05/2019 04:19 AM Tutorials: 1 Rating: 4.9/5

MATH221 Statistics for Decision Making

Week 4 Homework

Question 1 The
length of time a person takes to decide which shoes to purchase is normally
distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find
the probability that a randomly selected individual will take less than 5
minutes to select a shoe purchase. Is this outcome unusual?

Homework
Help:

4VA.
Calculating normal probabilities (Links to an external site.) (2:18)

4DA.
Description of normal distribution, area, and probabilities, definition of
unusual events (Links to an external site.) (DOCX)

Probability is 0.03, which is usual as it is
not less than 5%

Probability is 0.97, which is unusual as it
is greater than 5%

Probability is 0.03, which is unusual as it
is less than 5%

Probability is 0.97, which is usual as it is
greater than 5%

Question 2 Monthly
water bills for a city have a mean of $108.43 and a standard deviation of
$36.98. Find the probability that a randomly selected bill will have an amount
greater than $173, which the city believes might indicate that someone is
wasting water. Would a bill that size be considered unusual?

Homework
Help:

4VA.
Calculating normal probabilities (Links to an external site.) (2:18)

4DA.
Description of normal distribution, area, and probabilities, definition of
unusual events (Links to an external site.)(DOCX)

Probability is 0.04, which is unusual as it
is not less than 5%

Probability is 0.04, which is usual as it is
less than 5%

Probability is 0.04, which is unusual as it
is less than 5%

Probability is 0.04, which is usual as it is
not less than 5%

Question 3 In
a health club, research shows that on average, patrons spend an average of 42.5
minutes on the treadmill, with a standard deviation of 4.8 minutes. It is
assumed that this is a normally distributed variable. Find the probability that
randomly selected individual would spent between 30 and 40 minutes on the
treadmill.

Homework
Help:

4VA.
Calculating normal probabilities (Links to an external site.) (2:18)

4DA.
Description of normal distribution, area, and probabilities, definition of
unusual events (Links to an external site.)(DOCX)

0.70

Less than 1%

0.40

0.30

Question 4 A
tire company measures the tread on newly-produced tires and finds that they are
normally distributed with a mean depth of 0.98mm and a standard deviation of
0.35mm. Find the probability that a randomly selected tire will have a depth
less than 0.50mm. Would this outcome warrant a refund (meaning that it would be
unusual)?

Homework
Help:

4VA.
Calculating normal probabilities (Links to an external site.) (2:18)

4DA.
Description of normal distribution, area, and probabilities, definition of
unusual events (Links to an external site.)(DOCX)

Probability of 0.09 and would not warrant a
refund

Probability of 0.09 and would warrant a
refund

Probability of 0.91 and would warrant a
refund

Probability of 0.91 and would not warrant a
refund

Question 5 A
grocery stores studies how long it takes customers to get through the speed
check lane. They assume that if it takes more than 10 minutes, the customer
will be upset. Find the probability that a randomly selected customer takes
more than 10 minutes if the average is 7.45 minutes with a standard deviation
of 1.04 minutes.

Homework
Help:

4VA.
Calculating normal probabilities (Links to an external site.) (2:18)

4DA.
Description of normal distribution, area, and probabilities, definition of
unusual events (Links to an external site.)(DOCX)

0.007

0.501

0.993

0.071

Question 6 In
an agricultural study, the average amount of corn yield is normally distributed
with a mean of 185.2 bushels of corn per acre, with a standard deviation of
23.5 bushels of corn. If a study included 1100 acres, about how many would be
expected to yield more than 190 bushels of corn per acre?

Homework
Help:

4VB.
Calculating number from a sample that meet criteria based on normal
probabilities (Links to an external site.) (1:32)

419 acres

639 acres

503 acres

461 acres

Question 7 On
average, the parts from a supplier have a mean of 31.8 inches and a standard
deviation of 2.4 inches. Find the probability that a randomly selected part
from this supplier will have a value between 27.0 and 36.6 inches. Is this
consistent with the Empirical Rule of 68%-95%-99.7%?

Homework
Help:

4DB.
Connection between normal probabilities and Empirical Rule (Links to an
external site.) (DOCX)

Probability is 0.95, which is consistent with
the Empirical Rule

Probability is 0.95, which is inconsistent with
the Empirical Rule

Probability is 0.02, which is inconsistent
with the Empirical Rule

Probability is 0.98, which is inconsistent
with the Empirical Rule

Question 8 A
process is normally distributed with a mean of 10.2 hits per minute and a
standard deviation of 1.04 hits. If a randomly selected minute has 12.9 hits,
would the process be considered in control or out of control?

Homework
Help:

4VC.
Calculating probabilities from manufacturing to determine if system is in
control (Links to an external site.) (4:12)

Out of control as this one data point is more
than two standard deviations from the mean

In control as this one data point is not more
than three standard deviations from the mean

In control as only one data point would be
outside the allowable range

Out of control as this one data point is more
than three standard deviations from the mean

Question 9 The
candy produced by a company has a sugar level that is normally distributed with
a mean of 16.8 grams and a standard deviation of 0.7 grams. The company takes
readings of every 10th bar off the production line. The reading points are
17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 18.4. Is the process in control or out of
control and why?

Homework
Help:

4VC.
Calculating probabilities from manufacturing to determine if system is in
control (Links to an external site.) (4:12)

It is in control as two of three consecutive
data points are more than 2 standard deviations from the mean

It is in control as none of these data points
is more than 3 standard deviations from the mean

It is out of control as two of three
consecutive data points are more than 2 standard deviations from the mean

It is out of control as the values jump above
and below the mean

Question 10
The toasters produced by a company have a normally distributed life span with a
mean of 5.8 years and a standard deviation of 0.9 years, what warranty should
be provided so that the company is replacing at most 5% of their toasters sold?

Homework
Help:

4VD.
Calculating probabilities to compare to set probabilities such as warranties
and production guidelines (Links to an external site.) (2:23)

7.3 years

5.9 years

4.6 years

4.3 years

Question 11
A running shoe company wants to sponsor the fastest 5% of runners. You know
that in this race, the running times are normally distributed with a mean of
7.2 minutes and a standard deviation of 0.56 minutes. How fast would you need
to run to be sponsored by the company?

Homework
Help:

4VD.
Calculating probabilities to compare to set probabilities such as warranties
and production guidelines (Links to an external site.) (2:23)

8.3 minutes

8.1 minutes

6.3 minutes

6.1 minutes

Question 12
The weights of bags of peas are normally distributed with a mean of 12.08
ounces and a standard deviation of 1.03 ounces. Bags in the upper 5% are too
heavy and must be repackaged. What is the most that a bag can weigh and not
need to be repackaged?

Homework
Help:

4VD.
Calculating probabilities to compare to set probabilities such as warranties
and production guidelines (Links to an external site.) (2:23)

10.06 ounces

10.28 ounces

10.39 ounces

13.77 ounces

Question 13
A stock’s price fluctuations are approximately normally distributed with a mean
of $26.94 and a standard deviation of $3.54. You decide to sell whenever the
price reaches its highest 20% of values. What is the highest value you would
still hold the stock?

Homework
Help:

4VE.
Determining values from normal distributions based on probabilities (Links to
an external site.) (2:42)

4DC. Using
normal distributions and probabilities to determine set values (DOCX

$29.92

$30.48

$30.42

$23.96

Question 14
In a survey of first graders, their mean height was 50.4 inches with a standard
deviation of 3.55 inches. Assuming the heights are normally distributed, what
height represents the first quartile of these students?

Homework
Help:

4VE.
Determining values from normal distributions based on probabilities (Links to
an external site.) (2:42)

4DC. Using
normal distributions and probabilities to determine set values DOCX

52.79 inches

48.01 inches

43.30 inches

46.84 inches

Question 15
Hospital waiting room times are normally distributed with a mean of 38.12
minutes and a standard deviation of 8.63 minutes. What is the shortest wait
time that would still be in the worst 5% of wait times?

Homework Help:

4VE.
Determining values from normal distributions based on probabilities (Links to
an external site.) (2:42)

4DC. Using
normal distributions and probabilities to determine set values DOCX

46.75 minutes

23.92 minutes

52.32 minutes

29.49 minutes

Question 16
A machine set to fill soup cans with a mean of 20 ounces and a standard
deviation of 0.1 ounces. A random sample of 28 cans has a mean of 20.04 ounces.
Should the machine be reset?

Homework
Help:

4VF.
Calculating probabilities using the Central Limit Theorem (Links to an external
site.) (4:32)

4DD. Central
Limit Theorem, definition of unusual events (Links to an external site.) DOCX

No, the probability of this outcome at 0.017,
would be considered usual, so there is no problem

Yes, the probability of this outcome at 0.983
would be considered unusual, so the machine should be reset

No the probability of this outcome at 0.983
would be considered usual, so there is no problem

Yes, the probability of this outcome at
0.017, would be considered unusual, so the machine should be reset

Question 17
The length of timber cuts are normally distributed with a mean of 95 inches and
a standard deviation of 0.52 inches. In a random sample of 30 boards, what is
the probability that the mean of the sample will be between 94.7 inches and
95.3 inches?

Homework Help:

4VF.
Calculating probabilities using the Central Limit Theorem (Links to an external
site.) (4:32)

4DD.
Central Limit Theorem, definition of unusual events DOCX

0.436

0.950

0.998

0.002

Question 18
The Dow Jones Industrial Average has had a mean gain of 432 pear year with a
standard deviation of 722. A random sample of 40 years is selected. What is the
probability that the mean gain for the sample was between 200 and 500?

Homework
Help:

4VF. Calculating
probabilities using the Central Limit Theorem (Links to an external site.)
(4:32)

4DD.
Central Limit Theorem, definition of unusual events DOC

0.703

0.297

0.836

0.164

Question 19
Of all the companies on the New York Stock Exchange, profits are normally
distributed with a mean of $6.54 million and a standard deviation of $10.45
million. In a random sample of 73 companies from the NYSE, what is the
probability that the mean profit for the sample was between -2.9 million and
4.5 million?

Homework
Help:

4VF.
Calculating probabilities using the Central Limit Theorem (Links to an external
site.) (4:32)

4DD.
Central Limit Theorem, definition of unusual events DOCX

0.048

0.052

0.477

0.239

Question 20

Doing
research for insurance rates, it is found that those aged 30 to 49 drive an
average of 38.7 miles per day with a standard deviation of 6.7 miles. These
distances are normally distributed. If a group of 60 drivers in that age group
are randomly selected, what is the probability that the mean distance traveled
each day is between 29.9 miles and 39.9 miles?

Homework
Help:

4VF.
Calculating probabilities using the Central Limit Theorem (Links to an external
site.) (4:32)

4DD.
Central Limit Theorem, definition of unusual events DOCX

0.827

0.429

0.917

0.477