In the normal distribution with any given mean and standard deviation, we know that approximately

68% of the observations fall within one standard deviation of the mean

95% of the observations fall within two standard deviations of the mean

99.7% of the observations fall within 3 standard deviations of the mean.

This is sometimes called the 68-95-99.7 Empirical Rule of Thumb.

Using the 68-95-99.7Empirical Rule-of-Thumb, answer the following questions:

A study was designed to investigate the effects of two variables--(1) a student's level of mathematical anxiety and (2) teaching method--on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 450 with a standard deviation of 30 on a standardized test. The test scores follow a normal distribution.

a.True or False: The total area under the normal curve is one.

b.What percentage of scores would you expect to be greater than 390?%

c.What percent of the students, chosen at random, would have a score less than 300?Which of the following is the correct answer: is it close to 100% or close to 99.7% or close to 0%? The percent is closest to%.

d.What percentage of scores would you expect to be greater than 510?%

e.What percentage of scores would you expect to be between 390 and 510?