Question

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 14. Use the empirical rule to determine the following.

A.) What percentage of people has an IQ score between 86 and 114?

B,) What percentage of people has an IQ score less than 72 or greater than 128?

C.) What percentage of people has an IQ score greater than 142?

A.) ____% (Type an integer or a decimal).

B.) ____ % (Type an integer or a decimal).

C.) ____ (Type an integer or a decimal).

Answer 1

answer)

As the data is bell shaped that is normally distributed we can use the emperical rule to estimate the answers

According to the emperical rule

About 68% lies in between mean - s.d and mean + s.d

95% lies in between mean - 2*s.d and mean + 2*s.d

99.7% lies in between mean - 3*s.d and mean + 3*s.d

Mean = 100

And s.d = 14

So, 68% lies in between 100-14 and 100+14

That is in between 86 and 114

For part A answer is 68%

Now, 95% lies in between 72 and 128 (100-2*14, 100+2*14)

So, below 72 and above 128 there would be 2.5%

And we know that p(a or b) = p(a) + p(b)

So answer is 2.5 +2.5 = 5%

C)

Above 142

142 is = 100 + 3*14

Now 99.7% lies in between 58 and 142

So, above 142 there would be = 100 - 97.3)/2

= 0.15%