Exam 6: The Normal Distribution and Other Continuous Distributions

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 6-1 The manager of a surveying company believes that the average number of phone surveys completed per hour by her employees has a normal distribution. She takes a sample of 15 days output from her employees and determines the average number of surveys per hour on these days. The ordered array for this data is: 10.0, 10.1, 10.3, 10.5, 10.7, 11.2, 11.4, 11.5, 11.7, 11.8, 11.8, 12.0, 12.2, 12.2, 12.5. -Referring to Table 6-1, construct a normal probability plot for the data.

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.

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with µ = 110 grams and a = 25 grams. Approximately 83% of the vitamins will have at least how many grams of pyridoxine?

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. So, 90% of the products require more than _____minutes for assembly.

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 time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. Find the waiting time at which only 10% of the customers will continue to hold.

TABLE 6-7 A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.15. -Referring to Table 6-7, which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than 2 computers will require repair on a given day?

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because the probability of getting a specific value of a random variable is zero with the normal distribution.

TABLE 6-5 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 6-5, the probability is 75% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from the mean?

TABLE 6-2 The city manager of a large city believes that the number of reported accidents on any weekend has a normal distribution. She takes a sample of nine weekends and determines the number of reported accidents during each. The ordered array for this data is: 15, 46, 53, 54, 55, 76, 82, 256, 407. -Referring to Table 6-2, the seventh standard normal quantile is _____ .

As a general rule, one can use the normal distribution to approximate a binomial distribution whenever n(u - 1) is at least 5.

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes. What is the average number of arrivals per minute?

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

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%. The middle 60% of the time lapsed will fall between which two numbers?

TABLE 6-3 The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean 320 and population standard deviation 20 inches. -Referring to Table 6-3, a single Monday is chosen at random. State in which of the following ranges the number of column inches of classified advertisement is most likely to be:

The probability that a standard normal random variable, Z, is below 1.96 is 0.4750.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 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 random 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.

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

To determine the probability of getting fewer than 3 events of interest in a binomial distribution, you will find the area under the normal curve for X = 3.5 and below.