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, the probability is 0.10 that John's commission from the jewelry store is more than how much in a given month?

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, 17% of the products would be assembled within minutes.

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 80% of the time?

SCENARIO 6-4 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 6-4, find the probability that the annual return of a random year will be more than 11.5%.

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).

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 80% of the time?

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 and75?

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?

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 less than 20 minutes.

The probability that a standard normal variable, Z, is between 1.50 and 2.10 is the same as the probability Z is between - 2.10 and - 1.50.

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?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is between -2.33 and 2.33 is .

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 between $5,000 and $7,000?

A normal probability plot may be used to assess the assumption of normality for a set of data.

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 less than $13,000?

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 14 and 16 minutes.

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).

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 6-5 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?

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 less than 12 minutes.