Exam 6: The Normal Distribution and Other Continuous Distributions

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is more than 0.77 is .

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 6-6 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,what is the value above which will account for the highest 25% of the possible annual returns?

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 10 seconds after just being hit by a visitor?

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 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,the probability is 0.95 that John's commission from the jewelry store is at least how much in a given month?

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

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 between 100 and 120 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 values are larger than is 0.6985.

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 between the next 1.2 and 1.5 seconds after just being hit by a visitor?

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 more than 19 minutes.

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 or more than 120 grams of tea leaves?

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 between 7.5% and 11%.

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

The value of the cumulative standardized normal distribution at 1.5X is 0.9332.The value of X is

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

The amount of time between successive TV watching by first graders follows an exponential distribution with a mean of 10 hours.The probability that a given first grader spends less than 20 hours between successive TV watching is .

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 less than 10 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%.What is the probability of a score between 75 and 90?