Exam 6: The Normal Distribution and Other Continuous Distributions

TABLE 6-4 The interval between consecutive hits at a website is assumed to follow an exponential distribution with an average of 40 hits per minute. -The owner of a fish market determined that the average weight for a catfish is 3.2 pounds.He also knew that the probability of a randomly selected catfish that would weigh more than 3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%.The middle 40% of the catfish will weigh between ________ pounds and ________ pounds.

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 at least 100 grams of tea leaves?

The Tampa International Airport (TIA)has been criticized for the waiting times associated with departing flights.While the critics acknowledge that many flights have little or no waiting times,their complaints deal more specifically with the longer waits attributed to some flights.The critics are interested in showing,mathematically,exactly what the problems are.Which type of distribution would best model the waiting times of the departing flights at TIA?

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 over 125 inches in length?

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?

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute,find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

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 14 and 16 minutes.

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,17% of the products would be assembled within ________ minutes.

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 16 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 6-6,10% of the annual returns will be at least what amount?

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 10 and 12 minutes.

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 no more than 4.9 ounces of juices?

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 2.8 minutes (i.e.the mean number of calls answered in a minute is 1/2.8).What proportion of callers is put on hold longer than 2.8 minutes?

Suppose the probability of a car accident taking place anywhere on a stretch of a 20 miles highway is the same.Which of the following distributions would you use to determine the probability that a car accident will occur somewhere between the 5-mile and 15-mile posts of the highway?

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,for a given month,what is the probability that John's income as a waiter is no more than $300?

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 mean of the time interval?

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,for a given month,what is the probability that John's income as a waiter is between $800 and $900?

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 exactly 10 minutes?

TABLE 6-1 The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches. -Referring to Table 6-1,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

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 80 minutes?