Exam 6: The Normal Distribution

The data shown represent quiz scores from Ms. Mayer's 5th grade class. Use the Pearson coefficient to check for skewness. 21 25 9 21 23 22 22 15 23 22 16 11 20 20 17 22 21

Find the z value to the right of the mean such that 85% of the total area under the standard normal distribution curve lies to the left of it?

The number of standard deviations a particular X value is from the mean is commonly referred to as ________.

Find the probability using the standard normal distribution.

Which of the following characteristics does not apply to a theoretical normal distribution?

The area under the standard normal distribution curve to the right of z = 1.83 is 0.4664.

A(n) _______________________ is employed when a continuous distribution is used to approximate a discrete distribution.

In a standard normal distribution, what z value corresponds to 17% of the data between the mean and the z value?

To find the area under the standard normal distribution curve between two z values, one first finds the difference between the two z values, then locates the value corresponding to that difference in the Standard Normal Distribution table.

The area under a normal distribution curve is always positive even if the z value is negative.

The average age of vehicles registered in the United States is 96 months. Assume the population is normally distributed with a standard deviation of 15 months. Find the probability that the mean age of a sample of 36 vehicles is between 98 and 100 months?

Find the z value to the right of the mean so that 62.93% of the area under the distribution curve lies to the left of it.

X is a normally distributed random variable with a standard deviation of 3.50. Find the mean of X when 64.8% of the area lies to the left of 10.33. (Note: the diagram is not necessarily to scale.)

Find the z value that corresponds to the given area.

The difference between a sample mean and the population mean may be referred to as ______________________.

Find the probability using the standard normal distribution.

The average age of doctors in a certain hospital is 45.0 years old. Suppose the distribution of ages is normal and has a standard deviation of 4.0 years. If 16 doctors are chosen at random for a committee, find the probability that the average age of those doctors is less than 45.5 years. Assume that the variable is normally distributed.

As the sample size n increases, the shape of the distribution of the sample means taken with replacement from a population with mean $\mu$ and standard deviation $\sigma$ , will approach a normal distribution. This distribution will have a mean of $\mu$ and a standard deviation of . This is a statement of the _______________________.

Of the members of a Boy Scout troop, 15% have received the first aid merit badge. If 40 boy scouts are selected at random, find the probability that four or more will have the first aid merit badge?

The figure below is an example of a negatively skewed distribution.