Question

6) A certain standardized test has scores which range from 0 to 500, with decimal scores possible. Scores on the exam are normally distributed with a mean of 304 and a standard deviation of 42.

What proportion of students taking the exam receive a score that is within 74 points of the mean?

Round your answer to 4 decimal places.

Answer 1

Given,

= 304 , = 42

We convert this to standard normal as

P(X < x) = P(Z < ( x - ) / )

We have to calculate P ( 304 - 74 < X < 304 + 74) = ?

That is

P(230 < X < 378) = ?

P(230 < X < 378) = P(X < 378) - P(X < 230)

= P(Z < ( 378 - 304) / 42) - P(Z < ( 230 - 304) / 42)

= P(Z < 1.76) - P(Z < -1.76)

= 0.9608 - 0.0392 (From Z table)  

= 0.9216