Exam 6: The Normal Distribution and Other Continuous 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 6-2 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 a mean of $10,000 and a standard deviation of $2,000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with a mean of $1,000 and a standard deviation of $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 no more than $8,000?

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 standard deviation of the time interval?

The interval between patients arriving at an outpatient clinic follows an exponential distribution at a rate of 1 patient per hour.What is the probability of that randomly chosen arrival interval will be more than 1 hour?

TABLE 6-6 According to Investment Digest,the arithmetic mean of the annual return for common stocks over an 85-year period 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 6-3 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 between 10 and 20 minutes?

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 a mean of $10,000 and a standard deviation of $2,000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with a mean of $1,000 and a standard deviation of $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 6-2 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 a mean of $10,000 and a standard deviation of $2,000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with a mean of $1,000 and a standard deviation of $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 less than $1,300?

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 a mean of $10,000 and a standard deviation of $2,000.At night he works occasionally as a waiter,for which his monthly income is normally distributed with a mean of $1,000 and a standard deviation of $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 more than $9,500?

The interval between patients arriving at an outpatient clinic follows an exponential distribution at a rate of 1.5 patients per hour.What is the probability that a randomly chosen arrival interval will be between 10 and 15 minutes?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.So,85% of the possible Z values are smaller than ________.

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 less than 20 hours between successive TV watching 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%.The middle 86.64% of the students will score between which two scores?

TABLE 6-1 The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with a population mean of 320 and a population standard deviation of 20 inches. -Referring to Table 6-1,for a randomly chosen Monday,what is the probability that there will be between 280 and 360 column inches of classified advertisement?

TABLE 6-5 A company producing orange juice buys all of 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 juice?

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 14 and 17 seconds?

If a particular set of data is approximately normally distributed,we would find that approximately

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 6-3 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?

TABLE 6-6 According to Investment Digest,the arithmetic mean of the annual return for common stocks over an 85-year period 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?