Exam 6: The Normal Distribution and Other Continuous Distributions

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,above what weight (in pounds)do 89.80% of the weights occur?

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 to be more than 5 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 more than 4.2 ounces of juices?

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?

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

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 less than 124 inches?

The amount of time between successive TV watching by first graders follows an exponential distribution with a mean of 10 hours.The probability that a given first grader spends between 10 and 15 hours between successive TV watching is ________.

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 50 minutes?

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 take between 2 and 4.5 minutes to find a parking spot in the library parking lot.

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 between 3 and 5 pounds is ________.

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 longer than 17 seconds?

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,for a randomly chosen Monday,what is the probability there will be between 280 and 360 column inches of classified advertisement?

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,60% of the products would be assembled within ________ and ________ minutes (symmetrically distributed about the mean).

The "middle spread," that is the middle 50% of the normal distribution,is equal to one standard deviation.

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 4.5 and 5.2 ounces of juices?

The interval between patients arriving at an outpatient clinic follows an exponential distribution with mean 15 minutes.What is the probability that a randomly chosen arrival to be more than 18 minutes?

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 lower than 55?

The probability that a standard normal random variable,Z,falls between -1.50 and 0.81 is 0.7242.

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 commission from the jewelry store is between $11,000 and $12,000?

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 commission from the jewelry store will be between what two values symmetrically distributed around the population mean 90% of the time?