Question

PLEASEE HEEELP! In the normal distribution, 68% of the data lies within 1 standard deviation A: __/6 of the mean, 95% of the data lies within 2 standard deviations of the mean, and 99.7% of the data lies within 3 standard deviations of the mean. Answer the following question without using the Z-table. If scores on a test are normally distributed with mean 1100 and standard deviation 100, what percentage of the test scores are: a) more than 1300? b) less than 1100?

Answer 1

a) 2.5% b) 50%

Explanation:

1300 is two standard deviations higher than the mean. Since 95% of the data is covered within two standard deviations to the left and right of the mean, 5% is not covered. So, we have 2.5% leftover on the left side of the curve, under 900, and 2.5% leftover on the right side of the graph that is above 1300.

The mean is 1100, so anything above or below the mean is exactly 50% in a normal distribution.

Answer 2

Explanation:

This is the Empirical Rule.

68% of the data lies within 1 standard deviation of the mean, and so on.

If the mean is 1100 and the standard deviation is 100, 1300 represents two standard deviations above the mean. Using a calculator with distribution functions, we type in normcdf(2,10000), obtaining 0.023. This tells us that 2.3 percent of test scores are more than 1300.

Less than 1100: Since the mean is 1100, the area under the standard normal curve is exactly 0.5 (corresponding to 50% of data are less than 1100).