help with statistics hw please

Question

Scores of an IQ test have a​ bell-shaped distribution with a mean of

100 and a standard deviation of 20

Use the empirical rule to determine the following.

​(a) What percentage of people has an IQ score between

60 and 140?

​(b) What percentage of people has an IQ score less than

40 or greater than 160?

​(c) What percentage of people has an IQ score greater than

160?

I got A that is 95% i cant figure out b and c

Answer 1

Hey Maureen,

Nice work on part (a). The empirical rule stats that 95% of a normal distribution will be within 2 standard deviations

​(b) What percentage of people has an IQ score less than

40 or greater than 160?

For part (b) we want the percentage of people who fall outside of 3 standard deviations.

100 +/- (20*3) = 40 and 160. Since the empirical rule states that 99.7% of the population falls within 3 standard deviations. From this we find that 1-99.7 = .3% of the population falls outside of 3 standard deviations.

​(c) What percentage of people has an IQ score greater than 160?

This question is similar to (b), except this time we need to find the percentage of students in the upper side of the distribution outside of 3 standard deviations.

Since the distribution is normal we know that the two-tails will be equally distributed. If we account for the bottom tail of the distribution, we can find the percentage of students with IQ scores greater then 160.

We already found that .3% of students fall outside of 3 standard deviations. If we remove the students in the bottom tail of the distribution we are left with .15%. This is our answer

If you have anymore questions feel free message me. I'm always available to help students in need