Exam 6: The Normal Distribution and Other Continuous Distributions

SCENARIO 6-5 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 6-5, find the probability that the annual return of a random year will be less than 7.5%.

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 between 10 and 35 minutes?

The probability that a standard normal variable Z is positive is ________.

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 6-2 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?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So 96% of the possible Z values are between __________ and __________ (symmetrically distributed about the mean).

The value of the cumulative standardized normal distribution at Z is 0.6255. The value of Z is

SCENARIO 6-6 A recent survey revealed that American's Christmas spending averaged $830. Use this as the population mean American's Christmas spending. Suppose American's Christmas spending is normally distributed with a standard deviation of $220. -Referring to Scenario 6-6, for a randomly chosen American, what is the probability that he/she will spend less than $900 or more than $600 on Christmas spending?

SCENARIO 6-6 A recent survey revealed that American's Christmas spending averaged $830. Use this as the population mean American's Christmas spending. Suppose American's Christmas spending is normally distributed with a standard deviation of $220. -Referring to Scenario 6-6, for a randomly chosen American, the probability is 0.1 that he/she will spend less than how much on Christmas?

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, a single Monday is chosen at random. State in which of the following ranges the number of column inches of classified advertisement is most likely to be:

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 16 and 21 minutes.

SCENARIO 6-6 A recent survey revealed that American's Christmas spending averaged $830. Use this as the population mean American's Christmas spending. Suppose American's Christmas spending is normally distributed with a standard deviation of $220. -Referring to Scenario 6-6, 70% of Americans will spend at least how much on Christmas?

SCENARIO 6-6 A recent survey revealed that American's Christmas spending averaged $830. Use this as the population mean American's Christmas spending. Suppose American's Christmas spending is normally distributed with a standard deviation of $220. -Referring to Scenario 6-6, for a randomly chosen American, what is the probability that he/she will spend less than $1,000 on Christmas spending?

SCENARIO 6-6 A recent survey revealed that American's Christmas spending averaged $830. Use this as the population mean American's Christmas spending. Suppose American's Christmas spending is normally distributed with a standard deviation of $220. -Referring to Scenario 6-6, for a randomly chosen American, what is the probability that he/she will spend less than $500 or more than $1,300 on Christmas spending?

For some value of Z, the value of the cumulative standardized normal distribution is 0.2090. The value of Z is

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

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. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh less than 2.2 pounds is _______?

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?

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 90 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 15 and 21 minutes.