Exam 6: The Normal Distributions and Other Continuous Distributions

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, John's commission from the jewelry store will be between what two values symmetrically distributed around the population mean 90% of the time?

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?

The amount of tea leaves in a can from a production line is normally distributed with = 110 grams and = 25 grams.What is the probability that a randomly selected can will contain less than 100 grams or more than 120 grams of tea leaves?

The "middle spread," that is the middle 50% of the normal distribution, is equal to one standard deviation.

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%.The middle 86.64% of the students will score between which two scores?

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 time between arrivals at an intersection follows an exponential probability distribution with a mean of 14 seconds.What is the probability the arrival time between vehicles is 14 seconds or less ?

You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time elapsed between two consecutive trades will be between 13 and 14 seconds?

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, 90% of the products require more than __________ minutes for assembly.

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 standard deviation of the time interval?

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 no more than $300?

The value of the cumulative standardized normal distribution at Z is 0.8770.The value of Z is

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 more than 11.5%.

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 more than $9,500?

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 75% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from the mean?

You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time elapsed between two consecutive trades will be between 14 and 15 seconds?

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, 10% of the annual returns will be less than what amount?

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, the probability is 0.35 that John's income as a waiter is no less than how much in a given month?

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, what is the value above which will account for the highest 25% of the possible annual returns?

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 two values that will bound the middle 80% of the annual returns?