Exam 6: The Normal Probability Distribution

The mean and standard deviation of a normally distributed random variable which has been "standardized" are one and zero, respectively.

The total area under the curve f(x) of any continuous random variable x is equal to one.

The normal probability distribution is right-skewed for large values of the standard deviation , and is left-skewed for small values of .

The useful lifetime of a brand of automobile battery is normally distributed with mean 1,100 days and standard deviation 80 days. For how long should these batteries be guaranteed if the manufacturer wants to replace only five percent of the batteries sold because they "died" before the guarantee expired? ______________

Suppose z has a standard normal distribution. Then 28.1% of the possible z values are smaller than: ______________

Given that Z is a standard normal random variable, P(-1.2 Z 1.5) is:

Suppose x is normally distributed with a mean of 75 and a standard deviation of 4. Find the 90th percentile. ______________ Find the 95th percentile. ______________ Find the 5th percentile. ______________

A random variable x is normally distributed with a mean of 150 and a variance of 36. Given that x = 120, its corresponding z-score is 5.0.

If Z is a standard normal random variable, then the value z for which P(-z Z z) equals 0.8764 is:

Given that the random variable X is normally distributed with a mean of 80 and a standard deviation of 10, P(85 X 90) is:

For any random variable, P(x a) = P(x < a) because P(x = a) = 0.

Given a normal distribution with a mean of 80 and a standard deviation of 20, an observation of x = 50 corresponds to a standard normal deviate:

The time x a student spends learning a computer software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. A student is selected at random. What is the probability that the student spends less than 6 hours learning the software package? ______________ What is the probability that the student spends at least 8.5 hours learning the software package? ______________ What is the probability that the student spends between 6.5 and 8.5 hours learning the software package? ______________

A normal random variable x has an unknown mean and standard deviation. The probability that x exceeds 4 is 0.975, and the probability that x exceeds 5 is 0.95. Find . ______________ Find . ______________

If the z-value for a given value x of the random variable X is z = 1.96, and the distribution of X is normally distributed with a mean of 60 and a standard deviation of 6, to what x-value does this z-value correspond?

The relative frequency associated with a particular class in the population is the fraction of measurements in the population falling in that class.