Exam 6: The Normal Distribution and Other Continuous Distributions

The time between arrivals at an intersection follows an exponential probability distribution with a mean of 14 seconds.What is the probability the arrival time between vehicles is 7 seconds or less ?

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 75% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from the mean?

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,60% of the products would be assembled within and minutes (symmetrically distributed about the mean).

SCENARIO 6-6 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 6-6,find the two values that will bound the middle 80% of the annual returns?

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:

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?

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

The interval between patients arriving at an outpatient clinic follows an exponential distribution at a rate of 15 patients per hour.What is the probability that a randomly chosen arrival to be more than 5 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 less than $1300?

A company that receives most of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 2.8 minutes .What is the probability that a randomly selected caller is placed on hold fewer than 7 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 0.75 that John's commission from the jewelry store is less than how much in a given month?

SCENARIO 6-5 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 6-5,what is the probability that a randomly selected orange will contain no more than 4.2 ounces of juices?

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

The amount of tea leaves in a can from a production line is normally distributed with μ= 110 grams and σ= 25 grams.What is the probability that a randomly selected can will contain at least 100 grams of tea leaves?

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 less than 20 minutes.

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%.The middle 95.46% of the students will score between which two scores?

A company that receives most of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 3 minutes .Find the waiting time at which only 10% of the customers will continue to hold.

SCENARIO 6-7 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 6-7,what proportion of ball bearings has a diameter of greater than 6 mm? NEW QUESTION

The amount of tea leaves in a can from a production line is normally distributed with μ= 110 grams and σ= 25 grams.What is the probability that a randomly selected can will contain less than 100 grams of tea leaves?