Exam 6: The Normal Distribution

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 income as a waiter will be between what two values symmetrically distributed around the population mean 90% of the time?

For some value of Z, the value of the cumulative standardized normal distribution is 0.8340.The value of Z is

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.What is the probability that a randomly selected can will contain atleast 100 grams of tea leaves?

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 over125 inches in length?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,50% of the possible Z values are between and (symmetrically distributed about the mean).

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,27% of the possible Z values are smaller than .

SCENARIO 6-3 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 6-3, what is the probability that a randomly selected orange will contain between 4.2 and 4.9 ounces of juices?

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 longer than 17 seconds?

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%.The middle 86% of the time elapsed will fall between which two numbers?

Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.

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 75 and90?

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 standarddeviation of 3.5 years.What proportion of the plan recipients would receive payments beyond age75?

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 than95?

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

SCENARIO 6-5 Ball bearings are manufactured with a mean diameter of 6 millimeters (mm).Because of the inherent manufacturing process variability, the lots of bearings are approximately normally distributed with a standard deviation of 0.03 mm. -Using Scenario 6-5, if there is an order for 60,000 ball bearings and it states the bearing diameters must be between 5.96 and 6.04 mm, how many should the manager manufacture?

SCENARIO 6-5 Ball bearings are manufactured with a mean diameter of 6 millimeters (mm).Because of the inherent manufacturing process variability, the lots of bearings are approximately normally distributed with a standard deviation of 0.03 mm. -Using Scenario 6-5, what proportion of ball bearings has a diameter of more than 6.03 mm?

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?

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 isthat a product is assembled in between 15 and 21 minutes.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,85% of the possible Z values are smaller than .

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