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, for a given month, what is the probability that John's income as a waiter is less than $1300?

The probability that a standard normal variable, Z, is between 1.00 and 3.00 is0.1574.

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, 70% 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, the probability is 0.35 that John's income as a waiter is no less than how much in a given month?

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 probability is 20% that the time elapsed will be shorter how many seconds?

Any set of normally distributed data can be transformed to its standardized form.

If a set of data is approximately normally distributed, we would find that approximately

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 more than 11 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, for a given month, what is the probability that John's income as a waiter is between $800 and $900?

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.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is less than 1.15 is .

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 55 and95?

The probability that a standard normal variable, Z, falls between -2.00 and -0.44 is 0.6472.

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 lessthan 100 grams of tea leaves?

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 $9,000 and $11,000?

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot inthe library parking lot in less than 3 minutes.

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 .

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

A food processor packages orange juice in small jars.The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce.Find the proportion of all jars packaged by this process that have weights that fall below10.875 ounces.

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, any bearing having a diameter of less than 5.95 mm or greater than 6.05 mm are discarded.What proportion of the bearings will be discarded?