MATH 221 Week 4 Quiz 1

MATH 221 Week 4 Quiz 1 | Devry University

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

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

·         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%

 

 Question 2

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)  

·         Less than 1%    

·         0.30  

·         0.40  

·         0.70

 

 Question 3

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)?

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 0.97 and would warrant a refund  

·         Probability of 0.97 and would not warrant a refund  

·         Probability of 0.03 and would warrant a refund  

·         Probability of 0.03 and would not warrant a refund

 

Question 4

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)  

·         639 acres    

·         461 acres  

·         503 acres  

·         419 acres

 

 

Question 5

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%?

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 0.98, which is inconsistent with the Empirical Rule  

·         Probability is 0.02, which is inconsistent with the Empirical Rule  

·         Probability is 0.95, which is inconsistent with the Empirical Rule

 

 Question 6

In a normally distributed data set a mean of 55 where 95% of the data fall between 47.4 and 62.6, what would be the standard deviation of that data set?

4VG. Empirical Rule with examples (Links to an external site.) (4:38)

4DE. Standard scores and the Empirical Rule (Links to an external site.) (DOCX)  

·         1.9  

·         7.6  

·         5.7    

·         3.8

 

 Question 7

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?

4VG. Empirical Rule with examples (Links to an external site.) (4:38)

4DE. Standard scores and the Empirical Rule (Links to an external site.) (DOCX)  

·         95% based on the Empirical Rule  

·         95% based on the histogram  

·         68% based on the Empirical Rule  

·         68% based on the histogram

 

 Question 8

A process is normally distributed with a mean of 10.6 hits per minute and a standard deviation of 0.49 hits. If a randomly selected minute has 12.3 hits, would the process be considered in control or out of control?

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

·         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  

·         Out of control as this one data point is more than two 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?

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

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

·         It is out of control as at least 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    

·         It is in control as none of these data points is more than 3 standard deviations from 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 4% of their toasters sold?

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

·         6.8 years  

·         7.3 years    

·         4.2 years  

·         4.1 years

 

 Question 11

A running shoe company wants to sponsor the fastest 3% 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?

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

·         8.3 minutes  

·         6.3 minutes   

·         6.1 minutes  

·         8.1 minutes

 

 Question 12

A stock’s price fluctuations are approximately normally distributed with a mean of $29.51 and a standard deviation of $3.87. You decide to sell whenever the price reaches its highest 10% of values. What is the highest value you would still hold the stock?

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 (Links to an external site.) (DOCX)  

·         $30.00    

·         $34.47  

·         $33.38  

·         $24.55

 

 Question 13

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 15% of wait times?

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  

·         49.18 minutes  

·         36.49 minutes  

·         29.18 minutes    

·         47.06 minutes

 

 Question 14

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 94.8 inches and 95.8 inches?

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

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

·         0.982  

·         0.588  

·         0.098 

·         0.412

 

Question 15

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?

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  

·         0.015  

·         0.215  

·         0.105  

·         0.019