Answer to Question #197248 in Statistics and Probability for Hosea

Question

The Welcher Adult Intelligence Test Scale is composed of several subtexts. On one subtest the raw scores have a mean of 55 and a variance of 25.Assuming these raw scores are from a normal distribution.

a) what is the probability of obtaining a raw score between the mean and 46?

b)what is the probability of obtaining a raw score between 50 and 58?

Show all calculations!

Answer 1

$\mu=55,\sigma^2=25$

Standard deviation $=\sqrt{25}=5$

(a)  Probability of obtaining a raw score between the mean and 46-

z score for mean $z=\dfrac{55-55}{5}=0$

z-score for 46 $z=\dfrac{46-55}{5}=-1.8$

Probability is$=P(-1.8<z<0)=0.464$

(b) Probability of obtaining a raw score between 50 and 58-

$=P(50<X<58)\\[9pt]=P(\dfrac{50-55}{5}<z<\dfrac{58-55}{5})\\[9pt]=P(-1<z<0.6)\\[9pt]=0.567$