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 between -2.89 and -1.03 is ________.

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

Suppose the probability of finding a defective spot in an area on a piece of glass is the ratio of that area to the total area of the glass and the probability is the same across the whole glass.Which of the following distributions would you use to determine the probability of finding a defective spot in a randomly selected one square inch area on a piece of 10 feet by 10 feet glass?

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 3 minutes (i.e.the mean number of calls answered in a minute is ).What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

Suppose the light bulbs in a factory burn out at a rate of 50 bulbs per month.Which of the following distributions would you use to determine the probability that the next two light bulbs will burn out 2 days apart?

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 interval will be less than 10 minutes?

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 interval will be more than 5 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 between 100 and 110 grams of tea leaves?

True or False: Any set of normally distributed data can be transformed to its standardized form.

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,for a given month,what is the probability that John's income as a waiter is between $700 and $1,600?

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 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.

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 of tea leaves?

True or False: The probability that a standard normal variable,Z,falls between -2.00 and -0.44 is 0.6472.

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,for a given month,what is the probability that John's income as a waiter is between $1,200 and $1,600?

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 interval will be less than 20 minutes?

True or False: The probability that a standard normal variable,Z,is below 1.96 is 0.4750.

A food processor packages orange juice in small jars.The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce.Find the proportion of all jars packaged by this process that have weights that fall below 10.875 ounces.

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 variance of the time interval?

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 60 and 75?