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 probability that the time interval between two consecutive defective light bulbs will be at least 90 minutes?

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 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 6-2 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?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than 1.15 is ________.

Theoretically, the mean, median, and the mode are all equal for a normal distribution.

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?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is more than -0.98 is ________.

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).

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?

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What proportion of the plan recipients die before they reach the standard retirement age of 65?

A worker earns $15 per hour at a plant in China and is told that only 2.5% of all workers make a higher wage. If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour, the average wage for the plant is $7.50 per hour.

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 ________.

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

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 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 probability that the time interval between two consecutive defective light bulbs will be less than 10 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?

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 55 and 90?

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?

Let X represent the amount of time till the next student will arrive in the library parking lot at the university. If we know that the distribution of arrival time can be modeled using an exponential distribution with a mean of 4 minutes (i.e. the mean number of arrivals is 1/4 per minute), find the probability that it will take between 2 and 12 minutes for the next student to arrive at the library parking lot.