Exam 6: The Normal Distribution and Other Continuous Distributions

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 more than 7.5%.

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,the probability is 0.25 that John's income as a waiter is no more than how much in a given month?

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. -Referring to Table 6-4,what is the probability that the next hit at the website will occur within no sooner than 5 seconds after just being hit by a visitor?

Suppose students arrive at an advising office at a rate of 30 per hour.Which of the following distributions would you use to determine the probability that the next two students will arrive 30 minutes apart?

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 at least than $12,000?

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 probability that the time interval between two consecutive defective light bulbs will be between 10 and 20 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,the probability is 50% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from the mean?

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 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,70% of the products would be assembled within ________ 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 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 $1,200 and $1,600?

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 between 100 and 120 grams of tea leaves?

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 less than 12 minutes.

The probability that a standard normal random variable,Z,is between 1.00 and 3.00 is 0.1574.

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,the probability is 0.10 that John's commission from the jewelry store is more than how much in a given month?

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 that a randomly chosen arrival to be less than 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 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 more than $9,500?

It was believed that the probability of being hit by lightning is the same during the course of a thunderstorm.Which of the following distributions would you use to determine the probability of being hit by a lightning during the first half of a thunderstorm?

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 between 5 minutes and 15 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,15% of the products require more than ________ minutes for assembly.

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 $700 and $1600?