Exam 6: The Normal Distribution and Other Continuous Distributions

The probability that a standard normal random variable, Z, falls between -2.00 and -0.44 is 0.6472.

For some positive value of Z, the probability that a standard normal variable is between 0 and Z is 0.3770. The value of Z is:

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is between -2.33 and 2.33 is ________.

For some positive value of X, the probability that a standard normal variable is between 0 and +1.5X is 0.4332. The value of X 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 less than 20 minutes.

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

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes. What is the probability that a randomly chosen arrival to be more than 18 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 35 minutes?

A normal probability plot may be used to assess the assumption of normality for a particular batch of data.

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 probability that a standard normal random variable, Z, is below 1.96 is 0.4750.

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 15 and 16 seconds?

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 more than 11 minutes.

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be less than 15 minutes?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So 96% of the possible Z values are between ________ and ________ (symmetrically distributed about the mean).

For some positive value of X, the probability that a standard normal variable is between 0 and +2X is 0.1255. The value of X 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. Approximately 83% of the vitamins will have at least how many grams of tea leaves?

Patients arriving at an outpatient clinic follow 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?

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 of tea leaves?

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