Question

select then t, and drag to the Favorites Bar folder. Or import from another browser. Import favorites st: HW Normal Distribution ation of 100 and a standard deviation O of 15. Answer the following questi Suppose IQ scores are approximately normally distributed with a mean pts Not allowed. This test can only be taken once. tion This test can be saved and resumed later. mpletion Status

Answer 1

X: IQ score

X follows normal distribution with mean $\mu$ 100 and standard deviation $\sigma$ of 15

Question 1

What percent of the population has an IQ that is above average = P(X>$\mu$)

for a normal distribution, P(X$\leq$$\mu$) = P(X>$\mu$) = 50%

Question 2

Percent of population has an IQ below 110 = 100 x P(X<110)

Z-score for 110 = (110-$\mu$)/$\sigma$ = (110-100)/15 = 10/15 = 0.67

Z-score : 0.67

From standard normal tables, P(Z$\leq$0.67) = 0.7486

P(X<110) = P(Z$\leq$0.67) = 0.7486

Percent of population has an IQ below 110 = 100 x P(X<110) =100x 0.7486=74.86%

Ans :

Z-score : 0.67

percentage : 74.86%

Question 3

percent of population has an IQ above 130 =100x P(X>130)

P(X>130) =1 -P(X$\leq$130)

Z-score for 110 = (110-$\mu$)/$\sigma$ = (130-100)/15 = 30/15 = 2

Z-score : 2

From standard normal tables, P(Z$\leq$2) = 0.9772

P(X$\leq$130) = P(Z$\leq$2) = 0.9772

P(X>130) =1 -P(X$\leq$130)=1-0.9772 =0.0228

percent of population has an IQ above 130 =100x P(X>130)=100x0.0228=2.28%

Z-score for P(X$\leq$130)=2 ; Z-score for P(Z>130) = -2

percent of population has an IQ above 130 = 2.28%

Question 4

If an individual is randomly selected,

Probability that his/her IQ is between 110 and 130 = P(110$\leq$X$\leq$130) = P(X$\leq$130)-P(X$\leq$110)

From Question 2

P(X$\leq$110) = 0.7486

From Question 3

P(X$\leq$130) = 0.9772

P(110$\leq$X$\leq$130) = P(X$\leq$130)-P(X$\leq$110) =0.9772-0.7486=0.2286

Probability that his/her IQ is between 110 and 130 = 0.2286