MATH221 Week 4 Homework || with 100% Errorless
Solutions.
The length of time a person takes to decide which shoes to purchase is normally distributed with
a mean of 8.21 minutes and a standard deviation of 1.90. Find the probability that a randomly
selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome
unusual? correct answers Probability is 0.12, which is usual as it is not less than 5%
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. correct answers 0.30
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)? correct answers Probability of 0.09 and
would not warrant a refund
In an agricultural study, the average amount of corn yield is normally distributed with a mean of
189.3 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study
included 1200 acres, about how many would be expected to yield more than 180 bushels of corn
per acre? correct answers 785 acres
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. Use the Empirical Rule of 68%-95%-99.7% correct answers
Probability is 0.95
In a normally distributed data set a mean of 31 where 95% of the data fall between 27.4 and 34.6,
what would be the standard deviation of that data set? correct answers 1.8
In a normally distributed data set with a mean of 24 and a standard deviation of 4.2, what
percentage of the data would be between 19.8 and 28.2 and why? correct answers 68% based on
the Empirical Rule
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? Use a control chart to answer the question. correct answers In control as this
one data point is not more than three standard deviations from the mean
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 0.9 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, 19.4. Is the
process in control or out of control and why? Use a control chart to answer the question. correct
, answers It is in control as the data points more than 2 standard deviations from the mean are not
among three consecutive data points
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, the company is willing to have a warranty that
replaces at most 4% of their toasters sold. What is the longest a toaster can last and still be in the
lowest 4% of life spans correct answers 4.2 years
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 6.8 minutes and a standard deviation
of 0.37 minutes. How fast would you need to run to be sponsored by the company? correct
answers 6.2 minutes
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? correct answers $29.92
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
longest 15% of wait times? correct answers 47.06 minutes
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? correct answers 0.998
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 -2.8 million and 3.9 million? correct answers 0.015
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 6 minutes to select a shoe purchase. Is this outcome
unusual? correct answers Probability is 0.09, which is usual as it is not less than 5%
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 5.4 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. correct answers 0.31
A tire company measures the tread on newly-produced tires and finds that they are normally
distributed with a mean depth of 0.99mm and a standard deviation of 0.35mm. Find the
probability that a randomly selected tire will have a depth less than 0.31mm. Would this outcome
warrant a refund (meaning that it would be unusual)? correct answers Probability of 0.03 and
would warrant a refund
Solutions.
The length of time a person takes to decide which shoes to purchase is normally distributed with
a mean of 8.21 minutes and a standard deviation of 1.90. Find the probability that a randomly
selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome
unusual? correct answers Probability is 0.12, which is usual as it is not less than 5%
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. correct answers 0.30
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)? correct answers Probability of 0.09 and
would not warrant a refund
In an agricultural study, the average amount of corn yield is normally distributed with a mean of
189.3 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study
included 1200 acres, about how many would be expected to yield more than 180 bushels of corn
per acre? correct answers 785 acres
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. Use the Empirical Rule of 68%-95%-99.7% correct answers
Probability is 0.95
In a normally distributed data set a mean of 31 where 95% of the data fall between 27.4 and 34.6,
what would be the standard deviation of that data set? correct answers 1.8
In a normally distributed data set with a mean of 24 and a standard deviation of 4.2, what
percentage of the data would be between 19.8 and 28.2 and why? correct answers 68% based on
the Empirical Rule
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? Use a control chart to answer the question. correct answers In control as this
one data point is not more than three standard deviations from the mean
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 0.9 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, 19.4. Is the
process in control or out of control and why? Use a control chart to answer the question. correct
, answers It is in control as the data points more than 2 standard deviations from the mean are not
among three consecutive data points
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, the company is willing to have a warranty that
replaces at most 4% of their toasters sold. What is the longest a toaster can last and still be in the
lowest 4% of life spans correct answers 4.2 years
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 6.8 minutes and a standard deviation
of 0.37 minutes. How fast would you need to run to be sponsored by the company? correct
answers 6.2 minutes
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? correct answers $29.92
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
longest 15% of wait times? correct answers 47.06 minutes
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? correct answers 0.998
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 -2.8 million and 3.9 million? correct answers 0.015
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 6 minutes to select a shoe purchase. Is this outcome
unusual? correct answers Probability is 0.09, which is usual as it is not less than 5%
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 5.4 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. correct answers 0.31
A tire company measures the tread on newly-produced tires and finds that they are normally
distributed with a mean depth of 0.99mm and a standard deviation of 0.35mm. Find the
probability that a randomly selected tire will have a depth less than 0.31mm. Would this outcome
warrant a refund (meaning that it would be unusual)? correct answers Probability of 0.03 and
would warrant a refund
