Exam 6: The Normal Distribution and Other Continuous Distributions

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?

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 greater than 95?

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute,find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot.

Suppose students arrive at an advising office at a rate of 30 per hour.Which of the following distributions would you use to determine the probability that the next two students will arrive 30 minutes apart?

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 ________.

TABLE 6-1 The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with a population mean of 320 and a population standard deviation of 20 inches. -Referring to Table 6-1,for a randomly chosen Monday,what is the probability that there will be less than 340 column inches of classified advertisement?

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?

True or False: A worker earns $15 per hour at a plant in China and is told that only 2.5% of all workers make a higher wage.If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour,the average wage for the plant is $7.50 per hour.

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 more than 5 hours between successive TV watching is ________.

The value of the cumulative standardized normal distribution at 1.5X is 0.9332.The value of X is

TABLE 6-4 The interval between consecutive hits at a website is assumed to follow an exponential distribution with an average of 40 hits per minute. -Referring to Table 6-4,what is the probability that the next hit at the website will occur between the next 1.2 and 1.5 seconds after just being hit by a visitor?

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 less than 124 inches?

TABLE 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 a mean of $10,000 and a standard deviation of $2,000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with a mean of $1,000 and a standard deviation of $300.John's income levels from these two sources are independent of each other. -Referring to Table 6-2,the probability is 0.9 that John's income as a waiter is less than how much in a given month?

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 95?

TABLE 6-4 The interval between consecutive hits at a website is assumed to follow an exponential distribution with an average of 40 hits per minute. -Referring to Table 6-4,what is the probability that the next hit at the website will occur no sooner than 5 seconds after just being hit by a visitor?

TABLE 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 Table 6-6,find the two values that will bound the middle 80% of the annual returns.

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute,find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

True or False: A normal probability plot may be used to assess the assumption of normality for a particular set of data.

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.Find the age at which payments have ceased for approximately 86% of the plan participants.

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.So,15% of the products require more than ________ minutes for assembly.