Exam 6: The Normal Distribution and Other Continuous Distributions

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 and the result of the previous question,if 40,000 ball bearings were to be manufactured,how many would the manager have to discard?

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.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,27% of the possible Z values are smaller than .

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 between 15 and 21 minutes.

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 in the library parking lot in less than 3 minutes.

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 14 seconds?

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,15% of the products require more than minutes for assembly.

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 less than 15 minutes?

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed,the probability that a randomly selected catfish will weigh less than 2.2 pounds is ?

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 0.9 that John's income as a waiter is less 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 patient per hour.What is the probability that a randomly chosen arrival to be more than 2.5 hours?

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 at least 90 minutes?

The probability that a standard normal variable,Z,is between 1.50 and 2.10 is the same as the probability Z is between - 2.10 and - 1.50.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,50% of the possible Z values are between and (symmetrically distributed about the mean).

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?

If a data set is approximately normally distributed,its normal probability plot would be S-shaped.

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 14 seconds or less ?

The interval between patients arriving at an outpatient clinic follows an exponential distribution with mean 15 minutes.What is the mean number of arrivals per minute?

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 14 and 15 seconds?

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,for a randomly chosen Monday,what is the probability there will be less than 340 column inches of classified advertisement?