Distribution - Statistics - Quiz | Exercises Statistics

Q. We have a training program designed to upgrade the supervisory skill of production line

supervisors. Because the program is self administered, supervisor require different number of hours to

complete the program. A study of past participants indicates that the mean length of time spent on the

program is 500 hours and that this normally distributed random variable has standard deviation of 100

hours.

Suppose a training programme director wants to know the probability that a patient chosen at random

would require between 550 and 650 hours to complete the required work

Q2: The mean hourly pay rate for financial managers in the East North Central region is $32.62, and

the standard deviation is $2.32 (Bureau of Labor Statistics, September 2005). Assume that pay rates

are normally distributed.

a. What is the probability a financial manager earns between $30 and $35 per hour?

b. How high must the hourly rate be to put a financial manager in the top 10% with respect to

pay/

c. For a randomly selected financial manager, what is the probability the manager earned less

than $28 per hour?

Q3: The time needed to complete a final examination in a particular college course is normally

distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following

questions.

a. What is the probability of completing the exam in one hour or less?

b. What is the probability that a student will complete the exam in more than 60 minutes but less

than 75 minutes?

c. Assume that the class has 60 students and that the examination period is 90 minutes in length.

How many students do you expect will be unable to complete the exam in the allotted time?

Q.4 Jarrid Medical,Inc., is developing a compact kidney dialysis machine, but its chief engineer, mike

Crowe, is having trouble controlling the variability of rate at which fluid moves through the device.

Medical standard require that the hourly flow be 4 liters, plus or minus 0.1 liter, 80 percent of the

time. Mr. Crowe, in testing the prototype, has found that 68% of the time, the hourly flow is within

0.08 liter of the 4.2 liters. Does the prototype satisfy the medical standards?

Q4: When you sign up for a credit card, do you read the contract carefully? In FindLaw.com survey,

individuals were asked, “How closely do you read a contract for a credit card?” (USA Today, October

16, 2003). The findings were that 44% read every word, 33% read enough to understand the contract,

11% just glance at it, and 4% don’t read it at all.

a. For a sample of 500 people, how many would you expect to say that they read every word of

a credit card contract?

b. For a sample of 500 people, what is the probability that 200 or fewer will say they read every

word of a credit card contract?

c. For a sample of 500 people, what is the probability that at least 15 say they don’t read credit

card contracts?

Q5: The average annual amount American households spend for daily transportation is $6312

(Money, August 2001). Assume that the amount spent is normally distributed.

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Q. We have a training program designed to upgrade the supervisory skill of production line supervisors. Because the program is self administered, supervisor require different number of hours to complete the program. A study of past participants indicates that the mean length of time spent on the program is 500 hours and that this normally distributed random variable has standard deviation of 100 hours.

Suppose a training programme director wants to know the probability that a patient chosen at random would require between 550 and 650 hours to complete the required work

Q2: The mean hourly pay rate for financial managers in the East North Central region is $32.62, and the standard deviation is $2.32 (Bureau of Labor Statistics, September 2005). Assume that pay rates are normally distributed.

a. What is the probability a financial manager earns between $30 and $35 per hour? b. How high must the hourly rate be to put a financial manager in the top 10% with respect to pay/ c. For a randomly selected financial manager, what is the probability the manager earned less than $28 per hour?

Q3: The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions.

a. What is the probability of completing the exam in one hour or less? b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes? c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time?

Q.4 Jarrid Medical,Inc., is developing a compact kidney dialysis machine, but its chief engineer, mike Crowe, is having trouble controlling the variability of rate at which fluid moves through the device. Medical standard require that the hourly flow be 4 liters, plus or minus 0.1 liter, 80 percent of the time. Mr. Crowe, in testing the prototype, has found that 68% of the time, the hourly flow is within 0.08 liter of the 4.2 liters. Does the prototype satisfy the medical standards?

Q4: When you sign up for a credit card, do you read the contract carefully? In FindLaw.com survey, individuals were asked, “How closely do you read a contract for a credit card?” (USA Today, October 16, 2003). The findings were that 44% read every word, 33% read enough to understand the contract, 11% just glance at it, and 4% don’t read it at all.

a. For a sample of 500 people, how many would you expect to say that they read every word of a credit card contract? b. For a sample of 500 people, what is the probability that 200 or fewer will say they read every word of a credit card contract? c. For a sample of 500 people, what is the probability that at least 15 say they don’t read credit card contracts?

Q5: The average annual amount American households spend for daily transportation is $ (Money, August 2001). Assume that the amount spent is normally distributed.

a. Suppose you learn that 5% of American householders spend less than %1000 for daily transportation. What is the standard deviation of the amount spent? b. What is the probability that a household spends between $4000 and $6000? c. What is the range of spending for the 3% of households with the highest daily transportation cost?

Q6: According to Advertising Age, the average base salary for women working as copywriters in advertising firms is higher than the average base salary for men. The average base salary for women is $67000 and the average base salary for men is $65500 (Working Woman, July/August 2000). Assume salaries are normally distributed and that the standard deviation is $7000 for both men and women.

a. What is the probability of a woman receiving a salary in excess of $75000? b. What is the probability of a man receiving a salary in excess of $75000? c. What is the probability of a woman receiving a salary below $50000? d. How much would a woman have to make to have a higher salary than 99% of her male counterparts?

Q 7: A machine fills containers with a particular product. The standard deviation of filling weights is known from past data to be .6 ounce. If only 2% of the containers hold less than 18 ounces, what is the mean filling weight for the machine? That is, what must μ equal? Assume the filling weights have a normal distribution.

Q 8: A blackjack player at a Las Vegas casino learned that the house will provide a free room if play is for four hours at an average bet of $50. The player’s strategy provides a probability of .49 of winning on any one hand, and the player knows that there are 60 hands per hour. Suppose the player plays for four hours at a bet of $50 per hand.

a. What is the player’s expected pay off? b. What is the probability the player loses $1000 or more? c. What is the probability the player wins? d. Suppose the player starts with $1500. What is the probability of going broke?

Distribution - Statistics - Quiz, Exercises of Statistics

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Q. 9. The Gilbert Machinery Company has received a big order to produce electric motors

for a manufacturing company. In order to fit in its bearing, the drive shaft of the motor

must have a diameter of 5.1 ± 0.05 (inches). The company’s purchasing agents realizes

that there is a large stock of steel rods in inventory with mean diameter of 5.07”, and a

standard deviation of 0.07”. What is the probability of a steel rod from inventory fitting

the bearing?

Q. 10. Sixty-eight percent of the debt owed by American families is home mortgage or

equity credit (Federal Reserve Bulletin, January 1997). The median amount of mortgage

debt for families with the head of the household under 35 years old is $63,000. Assume

the amount of mortgage debt for this group is normally distributed and the standard

deviation is $15,000.

a. What is the mean amount of mortgage debt for this group?

b. How much mortgage debt do the 10% with the smallest debt have?

c. What percent of these families have mortgage debt in excess of $80,000?

d. The upper 5% of mortgage debt is in excess of what amount?