Exam 6: The Normal Distribution and Other Continuous Distributions

SCENARIO 6-3 Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. -Referring to Scenario 6-3,what is the probability that the time interval between two consecutive defective light bulbs will be at least 80 minutes?

The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes.The probability is that a product is assembled in between 14 and 16 minutes.

SCENARIO 6-6 According to Investment Digest,the arithmetic mean of the annual return for common stocks over an 85-year period was 9.5% but the value of the variance was not mentioned.Also 25% of the annual returns were below 8% while 65% of the annual returns were between 8% and 11.5%.The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric.Assume that this distribution is normal with the mean given above.Answer the following questions without the help of a calculator,statistical software or statistical table. -Referring to Scenario 6-6,75% of the annual returns will be lower than what value?

SCENARIO 6-2 John has two jobs.For daytime work at a jewelry store he is paid $15,000 per month,plus a commission.His monthly commission is normally distributed with mean $10,000 and standard deviation $2000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with mean $1,000 and standard deviation $300.John's income levels from these two sources are independent of each other. -Referring to Scenario 6-2,for a given month,what is the probability that John's commission from the jewelry store is between $5,000 and $7,000?

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition,you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score between 60 and 75?

SCENARIO 6-3 Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. -Referring to Scenario 6-3,the probability is 50% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from the mean?

SCENARIO 6-1 The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches. -Referring to Scenario 6-1,for a randomly chosen Monday,what is the probability there will be between 280 and 360 column inches of classified advertisement?

You were told that the mean score on a statistics exam is 75 with the scores normally distributed.In addition,you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%.What is the probability of a score between 90 and 95?

SCENARIO 6-6 According to Investment Digest,the arithmetic mean of the annual return for common stocks over an 85-year period was 9.5% but the value of the variance was not mentioned.Also 25% of the annual returns were below 8% while 65% of the annual returns were between 8% and 11.5%.The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric.Assume that this distribution is normal with the mean given above.Answer the following questions without the help of a calculator,statistical software or statistical table. -Referring to Scenario 6-6,find the probability that the annual return of a random year will be less than 7.5%.

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch.What proportion of the boards will be between 121 and 124 inches?

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan.Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years.What proportion of the plan recipients would receive payments beyond age 75?

The amount of time between successive TV watching by first graders follows an exponential distribution with a mean of 10 hours.The probability that a given first grader spends between 10 and 15 hours between successive TV watching is .

A normal probability plot may be used to assess the assumption of normality for a set of data.

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.A citation catfish should be one of the top 2% in weight.Assuming the weights of catfish are normally distributed,at what weight (in pounds)should the citation designation be established?

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan.Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years.What proportion of the plan recipients die before they reach the standard retirement age of 65?

The amount of tea leaves in a can from a production line is normally distributed with μ= 110 grams and σ= 25 grams.Approximately 83% of the can will have at least how many grams of tea leaves?

SCENARIO 6-3 Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. -Referring to Scenario 6-3,what is the probability that the time interval between two consecutive defective light bulbs will be exactly 10 minutes?

SCENARIO 6-4 The interval between consecutive hits at a web site is assumed to follow an exponential distribution with a mean of 40 hits per minute. -Referring to Scenario 6-4,what is the mean time between consecutive hits?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is between -2.33 and 2.33 is .

SCENARIO 6-2 John has two jobs.For daytime work at a jewelry store he is paid $15,000 per month,plus a commission.His monthly commission is normally distributed with mean $10,000 and standard deviation $2000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with mean $1,000 and standard deviation $300.John's income levels from these two sources are independent of each other. -Referring to Scenario 6-2,for a given month,what is the probability that John's income as a waiter is between $1,200 and $1,600?