Exam 6: The Normal Distribution and Other Continuous Distributions

Suppose the probability of producing a defective light bulb from a production line is the same over an interval of 90 minutes.Which of the following distributions would you use to determine the probability that a defective light bulb will be produced in a 15 minutes interval?

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 random 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 1/3).What proportion of customers having to hold more than 4.5 minutes will hang up before placing an order?

The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?

For some value of Z,the value of the cumulative standardized normal distribution is 0.8340.The value of Z is

The owner of a fish market determined that the average 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 more than 4.4 pounds is ________.

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 greater than 95?

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 random 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 1/3).What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?

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.

Suppose that past history shows that 60% of college students prefer Coca-Cola.A sample of 10,000 students is to be selected.Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola?

TABLE 6-6 According to Investment Digest,the arithmetic mean of the annual return for common stocks from 1926-2010 was 9.5% but the value of the variance was not mentioned.Also 25% of the annual returns were below 8% while 65% of the annual returns were between 8% and 11.5%.The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric.Assume that this distribution is normal with the mean given above.Answer the following questions without the help of a calculator,statistical software or statistical table. -Referring to Table 6-6,find the two values that will bound the middle 50% of the annual returns?

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 mean $10,000 and standard deviation $2,000.At night he works 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 Table 6-2,John's income as a waiter will be between what two values symmetrically distributed around the population mean 90% of the time?

Theoretically,the mean,median,and the mode are all equal for a normal distribution.

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 75 and 90?

The amount of juice that can be squeezed from a randomly selected orange out of a box of oranges with approximately the same size can most likely be modeled by which of the following distributions?

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 probability is 80% that the time lapsed will be longer than how many seconds?

TABLE 6-6 According to Investment Digest,the arithmetic mean of the annual return for common stocks from 1926-2010 was 9.5% but the value of the variance was not mentioned.Also 25% of the annual returns were below 8% while 65% of the annual returns were between 8% and 11.5%.The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric.Assume that this distribution is normal with the mean given above.Answer the following questions without the help of a calculator,statistical software or statistical table. -Referring to Table 6-6,find the probability that the annual return of a random year will be less than 11.5%.

TABLE 6-5 A company producing orange juice buys all its oranges from a large orange orchard.The amount of juice that can be squeezed from each of these oranges is approximately normally distributed with a mean of 4.7 ounces and some unknown standard deviation.The company's production manager knows that the probability is 30.85% that a randomly selected orange will contain less than 4.5 ounces of juice.Also the probability is 10.56% that a randomly selected orange will contain more than 5.2 ounces of juice.Answer the following questions without the help of a calculator,statistical software or statistical table. -Referring to Table 6-5,what is the probability that a randomly selected orange will contain between 4.2 and 4.9 ounces of juices?

The value of the cumulative standardized normal distribution at 1.5X is 0.9332.The value of X is

A wheel spinning game is played with a special wheel with 24 equal segments that determine the dollar values of a single spin.Which of the following distributions can best be used to compute the probability of winning a specific dollar value in a single spin?

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 die before they reach the standard retirement age of 65?