Answer to Question #311152 in Statistics and Probability for john

Question

A certain university produced 895 licensed teachers after they successfully passed the Licensure Examination for Teachers (LET). The professional Regulation Commission (PRC) records show that the examinees form that university posted an average rating of 85 with standard deviation of 2. If 36 successful examinees are selected at random, what is the probability that their ratings fall between 84 and 86?

Answer 1

Solution

Population mean $\mu =85$

Population s.d $\sigma=2$

(a) Probability that ratings fall between 84 and 86

$Z=\dfrac{X-\mu}{\sigma}$

$X_1=84 ~~and ~~X_2=86$

$Z_1=\dfrac{84-85}{2}=-0.5$

From normal distribution tables

$P(Z of -0.5) =0.30854$

$Z_2=\dfrac{86-85}{2}=0.5$

From normal distribution tables

$P(Z of 0.5)=0.69146$

For values above $86$

$P=1-0.69146=0.30854$

Probability that the values falls between 84 and 86

$=1-(0.30854+0.30854)$

$=0.38292$