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 values are larger than ________ is 0.3483.

TABLE 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 Table 6-3,what is the probability that the time interval between two consecutive defective light bulbs will be at least 50 minutes?

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

The amount of tea leaves in a can from a particular 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?

The amount of tea leaves in a can from a particular 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?

The interval between patients arriving at an outpatient clinic follows an exponential distribution with a mean of 15 minutes.What is the probability that a randomly chosen arrival interval will 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,17% of the products would be assembled within ________ minutes.

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.

TABLE 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 a mean of $10,000 and a standard deviation of $2,000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with a mean of $1,000 and a standard deviation of $300.John's income levels from these two sources are independent of each other. -Referring to Table 6-2,the probability is 0.45 that John's income as a waiter is more than how much in a given month?

A catalog company that receives the majority 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 (i.e.the mean number of calls answered in a minute is ).What proportion of callers is put on hold longer than 2.8 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,60% of the products would be assembled within ________ and ________ minutes (symmetrically distributed about the mean).

It was believed that the probability of being hit by lightning is the same during the course of a thunderstorm.Which of the following distributions would you use to determine the probability of being hit by lightning during the first half of a thunderstorm?

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

The amount of tea leaves in a can from a particular 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?

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time lapsed 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,70% of the products would be assembled within ________ minutes.

TABLE 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 a mean of $10,000 and a standard deviation of $2,000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with a mean of $1,000 and a standard deviation of $300.John's income levels from these two sources are independent of each other. -Referring to Table 6-2,John's commission from the jewelry store will be between what two values,symmetrically distributed around the population mean 90% of the time?

True or False: The probability that a standard normal variable,Z,is between 1.00 and 3.00 is 0.1574.

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 55 and 95?

TABLE 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 a mean of $10,000 and a standard deviation of $2,000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with a mean of $1,000 and a standard deviation of $300.John's income levels from these two sources are independent of each other. -Referring to Table 6-2,the probability is 0.25 that John's income as a waiter is no more than how much in a given month?