Question

A random sample of CO2 levels in a school has a sample mean of x¯=598.4 ppm and sample standard deviation of s=86.7 ppm. Use the Empirical Rule to determine the approximate percentage of CO2 levels that lie between 338.3 and 858.5 ppm. Round your answer to the nearest tenth.

Answer 1

99.7%

Explanation:

we start by getting the z-scores for the values given

We can get the z-scores using the formula below;

z-scores = (x-mean)/SD

for 338.5;

z = (338.5-598.4)/86.7 = -2.99 approximately-3

for 858.5;

z = (858.5-598.4)/86.7 = 3

so we want to get the percentages that lie within 3 standard deviations from the mean

According to the empirical rule, the percentages within 3 SD of the mean is;

100-0.15-0.15 = 99.7%