Exam 6: The Normal Distribution and Other Continuous Distributions

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 first standard normal quantile is ______ .

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, what is the probability that the time interval between two consecutive defective light bulbs will be less than 10 minutes?

One of the reasons that a correction for continuity adjustment is needed when approximating the binomial distribution with a normal distribution is because the normal distribution is used for a discrete random variable while the binomial distribution is used for a continuous random variable.

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 and assuming that the number of computers that requires repair on a given day follows a binomial distribution, compute the probability that there will be at least 25 computers that require repair on a given day using a normal approximation.

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 2.8 minutes. What is the probability that a randomly selected caller is placed on hold fewer than 7 minutes?

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, the data appear reasonably normal but not perfectly normal.

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, what is the probability that the time interval between two consecutive defective light bulbs will be at least 80 minutes?

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond age 75?

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. What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

As a general rule, one can use the normal distribution to approximate a binomial distribution whenever the sample size is at least 30.

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. What proportion of customers having to hold more than 4.5 minutes will hang up before placing an order?

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 90% 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 sixth standard normal quantile is______ .

A normal probability plot may be used to assess the assumption of normality for a particular batch of data.

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be between 121 and 124 inches?

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, the fourth standard normal quantile is _____.

TABLE 6-4 John has two jobs. For daytime work at a jewelry store he is paid $200 per month, plus a commission. His monthly commission is normally distributed with mean $600 and standard deviation $40. At night he works as a waiter, for which his monthly income is normally distributed with mean $100 and standard deviation $30. John's income levels from these two sources are independent of each other. -Referring to Table 6-4, for a given month, what is the probability that John's commission from the jewelry store is less than $640?

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 and assuming that the number of computers that requires repair on a given day follows a binomial distribution, compute the probability that there will be between 25 and 30 computers that require repair on a given day using a normal approximation.

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, what is the probability that the time interval between two consecutive defective light bulbs will be at least 90 minutes?

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, the ninth standard normal quantile is _____.