BUSI 230 HW 7.2 Applications of the Normal Distribution Assignment solutions complete answers

BUSI 230 HW 7.2 Applications of the Normal Distribution Assignment solutions complete answers 

 

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A value that is one standard deviation above the mean will be a -score of .

A value that is one standard deviation below the mean will be a -score of .

A value that is two standard deviations above the mean will be a -score of .

A value that is two standard deviations below the mean will be a -score of .

A value that is three standard deviations above the mean will be a -score of .

A value that is three standard deviations below the mean will be a -score of .

 

A normal population has mean u=9 and standard deviation =5.

(a) What proportion of the population is less than 19?

(b) What is the probability that a randomly chosen value will be greater than 4?

 

A normal population has mean u=37 and standard deviation =9.

(a) What proportion of the population is between 18 and 28?

(b) What is the probability that a randomly chosen value will be between 31 and 41?

 

A normal population has mean u = 57 and standard deviation = 8. What is the 87th percentile of the population? Use the TI-84 Plus calculator. Round the answer to at least one decimal place.

 

Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 11.7 pounds and standard deviation 2.9 pounds. Use Excel to answer the following. Round the answers to four decimal places.

(a) What proportion of babies weigh more than 14 pounds?

(b) What porportion of babies weigh less than 15 pounds?

(c) What proportion of babies weigh between 11.2 and 16 pounds?

(d) Is it unusual for a baby to weigh more than 17 pounds?

 

Check your blood pressure: In a recent study, the Centers for Disease Control and Prevention reported that diastolic blood pressures (in ) of adult women in the United States are approximately normally distributed with mean 80.6 and standard deviation 9.7.

(a) Find the 30th percentile of the blood pressures.

(b) Find the 33rd percentile of the blood pressures.

(c) Find the third quartile of the blood pressures.

 

Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 12 pounds and standard deviation 3.7 pounds.

(a) Find the 84th percentile of the baby weights.

(b) Find the 13th percentile of the baby weights.

The third quartile of the baby weights is  pounds.

 

Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean =41  and standard deviation  =6. Use the TI-84 Plus calculator to answer the following.

(a) What is the probability that a randomly chosen tire has a lifetime greater than 47 thousand miles?

(b) What proportion of tires have lifetimes between 36 and 45 thousand miles?

(c) What proportion of tires have lifetimes less than 44 thousand miles?

 

Tire lifetimes: The lifetime of a certain type of automobile tire (in thousands of miles) is normally distributed with mean  =41  and standard deviation  =5. Use the TI-84 Plus calculator to answer the following.

(a) Find the 16th percentile of tire lifetimes.

(b) Find the 68th percentile of tire lifetimes.

(c) Find the third quartile of the tire lifetimes.

(d) The tire company wants to guarantee that its tires will last at least a certain number of miles. What number of miles (in thousands) should the company guarantee so that only 3% of the tires violate the guarantee?