Exam 6: The Normal Distribution and Other Continuous Distributions

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 between 5 minutes and 15 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 commission from the jewelry store will be between what two values symmetrically distributed around the population mean 80% of the time?

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 mean of the time interval?

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 proportion of callers is put on hold longer than 2.8 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 between 82 and 100 grams of tea leaves?

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 lower than 55?

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 .

The probability that a standard normal variable,Z,is less than 5.0 is approximately 0.

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 more than $900?

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%.What is the probability that the time elapsed between two consecutive trades will be between 13 and 16 seconds?

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%.What is the probability that the time elapsed between two consecutive trades will be longer than 17 seconds?

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 interval between patients arriving at an outpatient clinic follows an exponential distribution at a rate of 1.5 patients per hour.What is the probability that a randomly chosen arrival to be between 10 and 15 minutes?

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

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 20 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 less than 11.5%.

Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2,find the probability that X is between 47 and 54.

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 6-5 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 between 4.5 and 5.2 ounces of juices?

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 6-6,10% of the annual returns will be less than what amount?