Answer to Question #180433 in Statistics and Probability for yuli noama

Question

1.    Scores on BMCC fall 2017 MAT150.5 department final exam form a normal distribution with a mean of 70 and a standard deviation of 8. What percent of the population has the following? 

 

a.    A score greater than 90

b.    A score between 60 and 85

c.    A score less than 60

Answer 1

$\mu=70,\sigma=8$

Let x denote the score

Using the formula to calculate z-score-

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

(a).$P(X>90)=P(z>\dfrac{90-70}{8})=P(z>2.5)=0.0062$

(b).$P(60<X<85)=P(\frac{60-70}{8}<Z<\dfrac{85-70}{8})=P(-1.25<z<1.75)=0.85429$

(c).$P(X<60)=P(z<\dfrac{60-70}{8})=P(z<-1.25)=0.10565$