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Homework answers / question archive / Question 1)   Find the probability using the standard normal distribution

Question 1)   Find the probability using the standard normal distribution

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Question 1)

 

Find the probability using the standard normal distribution. P(0 < z <1.96)

     

 

     
  • Question 2

 

   
 

Find the probability using the standard normal distribution. P(-1.23 < z < 0)

     

 

     
  • Question 3

 

   
 

Find the probability using the standard normal distribution. P(z > 0.82)

     

 

     
  • Question 4

 

   
 

Find the probability using the standard normal distribution. P(z < -1.77)

     

 

     
  • Question 5

 

   
 

Find the probability using the standard normal distribution. P(-0.20 < z < 1.56)

     

 

     
  • Question 6

 

   
 

Find the probability using the standard normal distribution. P(1.12 < z < 1.43)

     

 

     
  • Question 7

 

   
 

Find the probability using the standard normal distribution. P(z > -1.43)

     

 

     
  • Question 8

 

   
 

Find the z value to the right of the mean so that 54.78% of the area under the distribution curve lies to the left of it.

 

     

 

     
  • Question 9

 

   
 

Find the z value to the right of the mean so that 69.85% of the area under the distribution curve lies to the left of it.

 

     

 

     
  • Question 10

 

   
 

Find the z value to the right of the mean so that 88.10% of the area under the distribution curve lies to the left of it.

 

     

 

     
  • Question 11

 

   
 

The average commute time to work (one way) is 25 minutes according to the 2005 American Community Survey. If we assume that commute times are normally distributed and that the standard deviation is 6.1 minutes, what is the probability that a randomly selected commuter spends more than 30 minutes commuting one way?

Put answer in decimal m. Do not round. Use all four digits from the table. Do not give it in percentage m.

     

 

     
  • Question 12

 

   
 

 

The average commute time to work (one way) is 25 minutes according to the 2005 American Community Survey. If we assume that commute times are normally distributed and that the standard deviation is 6.1 minutes, what is the probability that a randomly selected commuter spends less than 18 minutes commuting one way?

Put answer in decimal m. Do not round. Use all four digits from the table. Do not give it in percentage m.

 

     

 

     
  • Question 13

 

   
 

The average monthly mortgage payment including principal and interest is $982 in the United States. If the standard deviation is approximately $180 and the mortgage payments are approximately normally distributed, find the probability that a randomly selected monthly payment is more than $1000?

State your answer in decimal m. Do not round. Do not give in percentage m.

 

     

 

     
  • Question 14

 

   
 

The average monthly mortgage payment including principal and interest is $982 in the United States. If the standard deviation is approximately $180 and the mortgage payments are approximately normally distributed, find the probability that a randomly selected monthly payment is more than $1475?

State your answer in decimal m. Do not round. Do not give in percentage m.

     

 

     
  • Question 15

 

   
 

The average monthly mortgage payment including principal and interest is $982 in the United States. If the standard deviation is approximately $180 and the mortgage payments are approximately normally distributed, find the probability that a randomly selected monthly payment is between $800 and $1150?

State your answer in decimal m. Do not round. Do not give in percentage m. 

     

 

     
  • Question 16

 

   
 

The average time a visitor spends at the Renzie Park Art Exhibit is 62 minutes. The standard deviation is 12 minutes. If a visitor is selected at random, find the probability that he or she will spend the following amount of time at the exhibit. Assume the variable is normally distributed. Please put in percent m.

a. At least 82 minutes.

     

 

     
  • Question 17

 

   
 

The average time a visitor spends at the Renzie Park Art Exhibit is 62 minutes. The standard deviation is 12 minutes. If a visitor is selected at random, find the probability that he or she will spend the following amount of time at the exhibit. Assume the variable is normally distributed. Please put in percent m.

b. At most 50 minutes.

     

 

     
  • Question 18

 

   
 

The average time a person spends at Barefoot Landing Seaquarium is 96 minutes. The standard deviation is 17 minutes. Assume the variable is normally distributed. If a visitor is selected at random, find the probability that he or she will spend the following time at the seaquarium. Please put answer in decimal m.

a. At least 120 minutes.

     

 

     
  • Question 19

 

   
 

The average time a person spends at Barefoot Landing Seaquarium is 96 minutes. The standard deviation is 17 minutes. Assume the variable is normally distributed. If a visitor is selected at random, find the probability that he or she will spend the following time at the seaquarium. Please put answer in decimal m.

b. At most 80 minutes.

     

 

     
  • Question 20

 

   
 

In order to help students improve their reading, a school district decides to implement a reading program. It is to be administered to the bottom 5% of the students in the district, based on the scores on a reading achievement exam. If the average score  the students in the district is 122.6, find the cutoff score that will make a student eligible  the program. The standard deviation is 18. Assume the variable is normally distributed. Round to two decimal places.

     

 

     
  • Question 21

 

   
 

A mandatory competency test  high school sophmores has a normal distribution with a mean of 400 and a standard deviation of 100.

a. The top 3% of students receive $500.00. What is the minimum score you would need to receive this award?

     
       
  • Question 22

 

   
 

A mandatory competency test  high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100.

b . The bottom 1.5% of students must go to summer school. What is the minimum score you would need to stay out of this group?

     

 

 
     
  • Question 23

 

   
 

A survey found that Americans generate an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 55 families will be between 17 and 18 pounds. Please put you answer in decimal m.

     

 

     
  • Question 24

 

   
 

A recent study of the lifetimes of cell phones found the average is 24.3 months. The standard deviation is 2.6 months. If a company provides its 33 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8. Assume cell phone life is normally distributed variable.

Please put you answer in decimal m.

     

 

     
  • Question 25

 

   
 

Assume that the mean systolic blood pressure of normal adults is 120 millimeters of mercury (mm Hg) and the standard deviation is 5.6. Assume the variable is normally distributed. Please put you answer in decimal m.

a. If an individual is selected, find the probability that the individual's blood pressure will be between 120 and 121.8 mm Hg.

     

 

     
  • Question 26

 

   
 

Assume that the mean systolic blood pressure of normal adults is 120 millimeters of mercury (mm Hg) and the standard deviation is 5.6. Assume the variable is normally distributed. Please put you answer in decimal m.

b. If a sample of 30 adults is selected, find the probability that the sample mean will be between 120 and 121.8 mm Hg.

     

 

     
  • Question 27

 

   
 

At a large publishing company, the mean age of proofreaders is 36.2 years, and the standard deviation is 3.7 years. Assume the variable is normally distributed. Please put you answer in decimal m.

a. If a proofreader from the company is randomly selected, find the probability that his or her age will be between 36 and 37.5 years.

     

 

     
  • Question 28

 

   
 

At a large publishing company, the mean age of proofreaders is 36.2 years, and the standard deviation is 3.7 years. Assume the variable is normally distributed. Please put you answer in decimal m.

b. If a random sample of 15 proofreaders is selected, find the probability that the mean age of the proofreaders in the sample will be between 36 and 37.5 years.

     

 

     

 

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