Exam 6: The Normal Probability Distribution

Examples of continuous probability distributions include the normal probability distribution, the Poisson probability distribution, and the binomial probability distribution.

Which of the following probability distributions can be used to describe the distribution for a continuous random variable?

Suppose z has a standard normal distribution. Then 59.9% of the possible z values are between ______________ and ______________ (symmetrically distributed around the mean).

Using the standard normal curve, the z-score representing the 95th percentile is 1.645.

The z-score representing the 99th percentile of the standard normal curve is 3.0.

Continuous random variables can assume infinitely many values corresponding to points on a line interval.

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

Given that Z is a standard normal random variable, what is the value z if the area to the right of z is 0.1949?

Which of the following incorrectly describes the discrete probability distributions and continuous probability density functions?

A normal random variable x has an unknown mean and standard deviation = 2.5. If the probability that x exceeds 7.5 is 0.8289, find . ______________

EPA studies of fuel consumption indicate compact car mileage to be normally distributed with a mean of 25.5 miles per gallon and a standard deviation of 5.0 mpg. What percentage of compact cars gets between 20 and 40 mpg? ______________

If Z is a standard normal random variable, the area between z = 0.0 and z = 1.50 compared to the area between z = 1.5 and z = 3.0 will be:

The mean and variance of any normal distribution are always zero and one, respectively.

All binomial distributions can be approximated very closely by normal distributions.

Using the standard normal table, the total probabilities to the right of z = 2.0 and to the left of z = -2.0 is:

A continuous random variable x is normally distributed with a mean of 100 oz. and a standard deviation of 20 oz. Given that x = 120, its corresponding z-score is -1.0.

A normal random variable x is standardized by expressing its value as the number standard deviations it lies to the right or left of its mean .

For a continuous random variable x, the probabilities P(0 x 1) and P(0 < x < 1) are always equal.

The left half of the normal curve is slightly smaller than the right half.

Suppose z has a standard normal distribution. Then 16.6% of the possible z values are larger than: ______________