Answer to Question #202190 in Statistics and Probability for ADRI

Question

A normal distribution has u=80 o=10. What is the probability of random selecting the following scores ?

a) x>75

b) x<85

c)between the mean of score of 90

d) between the mean of score of 50

e) 75< x >85

Answer 1

Given,

$\mu=80\\\sigma=10$

(a) $P(X>75)$

$z=\dfrac{X-\mu}{\sigma}=\dfrac{75-80}{10}=-0.5$

Using Standard normal distribution table:

So, $P(X>75)=P(z>-0.5)=0.6915$

(b) $P(X<85)$

$z=\dfrac{X-\mu}{\sigma}=\dfrac{85-80}{10}=0.5$

Using Standard normal distribution table:

So, $P(X<85)=P(z<0.5)=0.6915$

(c) between the mean and score of 90

$z_1=\dfrac{X-\mu}{\sigma}=\dfrac{80-80}{10}=0$

$z_2=\dfrac{X-\mu}{\sigma}=\dfrac{90-80}{10}=1$

Using Standard normal distribution table:

$P(0<z<1)=0.3413$

(d) between the mean and score of 50

$z_1=\dfrac{X-\mu}{\sigma}=\dfrac{80-80}{10}=0$

$z_2=\dfrac{X-\mu}{\sigma}=\dfrac{50-80}{10}=-3$

Using Standard normal distribution table:

$P(-3<z<0)=0.4987$

(e) 75 < x <85

$z_1=\dfrac{X-\mu}{\sigma}=\dfrac{75-80}{10}=-0.5$

$z_2=\dfrac{X-\mu}{\sigma}=\dfrac{85-80}{10}=0.5$

Using Standard normal distribution table:

$P(75<X<85)=P(-0.5<z<0.5)=0.3829$