Exam 6: The Normal Distribution

What is the z value such that 50% of the total area under the standard normal distribution curved lies to the right of it?

A biologist estimates that 40% of the deer in a region carry a certain type of tick. For a sample of 300 deer selected at random, what is the chance that 124 or fewer deer have this tick?

Find the probability using the standard normal distribution.

Find the area under the standard normal distribution curve between and .

A magazine reported that 6% of American drivers admit to reading the newspaper while driving. If 500 drivers are selected at random, find the probability that exactly 40 will admit to reading the newspaper while driving.

The standard deviation of a normal distribution is 20. What is the standard error of the mean obtained by averaging 225 samples?

Stating that the area under the standard normal distribution curve between z = 0 and z = 1.00 is 0.3413, is the same as stating that the _____________ of randomly selecting a standard normally distributed variable z with a value between 0 and 1.00 is 0.3413.

Find the area under the standard normal distribution curve between z = -2.05 and z = 2.05.

X is a normally distributed random variable with a standard deviation of 2.00. Find the mean of X if 12.71% of the area under the distribution curve lies to the right of 8.28. (Note: the diagram is not necessarily to scale.)

For a normal distribution with a mean of 4 and a standard deviation of 2, the value 5 has a z value of

One normal curve has a mean of 20 and a standard deviation of 5. A second normal curve has a mean of 5 and a standard deviation of 20. The curve that is more dispersed, or spread out, is

When the majority of the data values fall to the right of the mean, the distribution is said to be left-skewed.

Find the z value that corresponds to the given area.

Find the area under the standard normal distribution curve between z = 0 and z = 2.16.

At a large department store, the average number of years of employment for a cashier is 5.7 with a standard deviation of 1.8 years, and the distribution is approximately normal. If an employee is picked at random, what is the probability that the employee has worked at the store for over 10 years?

Mrs. Smith's reading class can read an average of 175 words per minute with a standard deviation of 20 words per minute. The top 3% of the class is to receive a special award. What is the minimum number of words per minute a student would need to read in order to get the award? Assume the data is normally distributed.

The average diameter of sand dollars on a certain island is 3.50 centimeters with a standard deviation of 1.00 centimeters. If 25 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 3.28 centimeters. Assume that the variable is normally distributed.

In order to have the standard error of the mean be 11, one would need to take _______ samples from a normally distributed population with a standard deviation of 55.

X is a normally distributed random variable with a mean of 10.00. If the probability that X is less than 11.54 is 0.67 (as shown below), then what is the standard deviation of X? (Note: the diagram is not necessarily to scale.)

Find the probability P(-0.77 < z < -0.16) using the standard normal distribution.