Question

For a given population of high school seniors, the Scholastic Aptitude Test (SAT) in mathematics has a mean score of 500 with a standard deviation of 100. Assume that the SAT scores are normally distributed. What is the probability that a randomly selected high school senior's score on mathe- matics part of SAT will be
(a) more than 675?
b) between 450 and 675?

Answer 1

Answer:

The probability that a randomly selected high school senior's score on mathematics part of SAT will be

(a) more than 675 is 0.0401

(b)between 450 and 675 is 0.6514

Step-by-step explanation:

Mean of Sat =$\mu = 500$

Standard deviation = $\sigma = 100$

We will use z score over here

 What is the probability that a randomly selected high school senior's score on mathe- matics part of SAT will be

(a) more than 675?

P(X>675)

$Z=\frac{x-\mu}{\sigma}\\Z=\frac{675-500}{100}$

Z=1.75

P(X>675)=1-P(X<675)=1-0.9599=0.0401

b)between 450 and 675?

P(450<X<675)

At x = 675

$Z=\frac{x-\mu}{\sigma}\\Z=\frac{675-500}{100}$

Z=1.75

At x = 450

$Z=\frac{x-\mu}{\sigma}\\Z=\frac{450-500}{100}$

Z=-0.5

P(450<X<675)=0.9599-0.3085=0.6514

Hence the probability that a randomly selected high school senior's score on mathematics part of SAT will be

(a) more than 675 is 0.0401

(b)between 450 and 675 is 0.6514