Exam 6: The Normal Distribution and Other Continuous Distributions

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 between $500 and $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, the middle 75% of Americans will spend how much on Christmas?

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, 75% of the annual returns will be lower than what value?

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 at least $700 on Christmas spending?

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 6-6 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 0.9 that he/she will spend at least how much on Christmas?

SCENARIO 6-4 A company producing orange juice buys all its oranges from a large orange orchard. The amount of juice that can be squeezed from each of these oranges is approximately normally distributed with a mean of 4.7 ounces and some unknown standard deviation. The company's production manager knows that the probability is 30.85% that a randomly selected orange will contain less than 4.5 ounces of juice. Also the probability is 10.56% that a randomly selected orange will contain more than 5.2 ounces of juice. Answer the following questions without the help of a calculator, statistical software or statistical table. -Referring to Scenario 6-4, what is the probability that a randomly selected orange will contain between 4.5 and 5.2 ounces of juices?

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 lower than 55?

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 0.9 that he/she will spend less than how much on Christmas?

Theoretically, the mean, median, and the mode are all equal for a normal distribution.

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, 80% of Americans will spend no more than how much on Christmas?

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds. He also knew that the probability of a randomly selected catfish that would weigh more than 3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%. The middle 40% of the catfish will weigh between ______ pounds and ______ pounds.

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 90% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from the mean?

If a data set is approximately normally distributed, its normal probability plot would be S-shaped.

You were told that the amount of time lapsed 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 lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. The middle 86% of the time lapsed will fall between which two numbers?

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 0.25 that John's income as a waiter is no more than how much in a given month?

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, 20% of American will spend more than how much on Christmas?

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 at least $1400?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z values are larger than __________ is 0.3483.

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?