Exam 6: The Normal Distributions and Other Continuous Distributions

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 50% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from 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 probability that the annual return of a random year will be more than 7.5%.

SCENARIO 6-4 The interval between consecutive hits at a web site is assumed to follow an exponential distribution with a mean of 40 hits per minute. -Referring to Scenario 6-4, what is the probability that the next hit at the web site will occur within no sooner than 5 seconds after just being hit by a visitor?

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, 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?

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?

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 and 90?

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 12 minutes.

Let X represent the amount of time till the next student will arrive in the library parking lot at the university.If we know that the distribution of arrival time can be modeled using an exponential distribution with a mean of 4 minutes (i.e.the mean number of arrivals is 1/4 per minute), find the probability that it will take between 2 and 12 minutes for the next student to arrive at the library parking lot.

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 than 95?

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?

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:

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?

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, what is the probability that the time interval between two consecutive defective light bulbs will be between 10 and 35 minutes?

Which of the following about the normal distribution is not true?

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 more than 6.03 mm?

The interval between patients arriving at an outpatient clinic follows an exponential distribution with mean 15 minutes.What is the probability that a randomly chosen arrival to be more than 18 minutes?

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 0.30 that John's commission from the jewelry store is no more than how much in a given month?

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, what is the variance of the time interval?

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 no more than $8,000?