Question

Question Help Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 61 and 139? (b) What percentage of people has an IQ score less than 74 or greater than 126? (c) What percentage of people has an IQ score greater than 1262 (a) % (Type an integer or a decimal) Enter your answer in the answer box and then click Check Answer у 2 parts Clear All remaining javascript.doExercise Te to search 0 e

Answer 1

a.

μ ± 3σ = μ ± 3σ = 100 ± 3*13 = 61 , 139

According to emprical rule, 99.7% data lies with the 3σ from the mean.

Ans = 99.7 %

b.

μ ± 2σ = 100 ± 2*13 = 74 , 126

According to emprical rule 95% data lies within the 2σ from the mean.

Ans = 95%

c.

A = 100, 0 = 13 We need to compute Pr(X > 126). The corresponding z-value needed to be computed is: X - 126 - 100 Z= 2 o 13 Therefore, we get that Pr(x > 126) = Pr (2) 126 – 100 13 = Pr(Z > 2) =1-0.9772 = 0.0228 The following is obtained graphically: Normal Distribution: Pr(X>126)=0.0228 0.035 0.030 0.025 1 0.020 0.015 A 0.010 0.005 0.000 0 20 40 50 80 100 120 140 160

Ans = 2.28%

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