Exam 6: The Normal Distribution and Other Continuous Distributions

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 variance of the time interval?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is more than 0.77 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 ________.

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 more than $900?

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

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 90 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 between 10 and 20 minutes?

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 to be less than 10 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, 60% of the products would be assembled within ________ and ________ minutes (symmetrically distributed about the mean).

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 middle 86% of the time lapsed will fall between which two numbers?

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 ________.

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 less than 100 grams or more than 120 grams of tea leaves?

The probability that a standard normal random variable, Z, is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.

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 6-6 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?

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, 75.8% of the college students will take more than how many minutes when trying to find a parking spot in the library parking lot?

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 0.35 that John's income as a waiter is no less than how much in a given month?

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.

The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. A batch of 100,000 such alarms was produced by independent production lines. Which of the following distributions would you use to figure out the probability that at least 90,000 of them will function properly in case of a fire?

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?