Question

QUESTION 6 The mean IQ score of all adults is 100, with a standard deviation of 15. Find the percentage of adults with scores between 70 and 130. Assume the data has a bell-shaped distribution. State the answer only and no additional work. Do not state the percent sign and state as a whole number. (Example: do not state 13% or 0.13. Instead state the answer as 13)

Answer 1

Question 6

Solution:

We are given that the data has a bell shaped (normal) distribution.

Mean = 100

SD = 15

We have to find P(70<X<130)

P(70<X<130) = P(X<130) – P(X<70)

Z = (X – mean) / SD

First find P(X<130)

Z = (130 – 100) / 15

Z = 30/15 = 2

P(Z<2) = P(X<130) = 0.97725

(By using z-table)

Now, find P(X<70)

Z = (70 – 100)/15

Z = -2

P(Z<-2) = P(X<70) = 0.02275

(By using z-table)

P(70<X<130) = P(X<130) – P(X<70)

P(70<X<130) = 0.97725 – 0.02275

P(70<X<130) = 0.9545

Answer: 95

Question 4

We are given

Data follows bell shaped distribution or normal distribution.

Mean = 72

SD = 5

X = 65

Z = (X – mean) / SD

Z = (65 – 72) / 5

Z = -7/5

Z = -1.4

Answer: -1.4