Question

Use the normal distribution of SAT critical reading scores for which the mean is 506 and the standard deviation is 107. Assume the variable x is normally distributed.

What percent of the SAT verbal scores are less than 600​?

If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than 525​?

Approximately( ) of the SAT verbal scores are less than 600. ​(Round to two decimal places as​ needed.)

You would expect that approximately ( ) SAT verbal scores would be greater than 525. ​(Round to the nearest whole number as​ needed.)  

Answer 1

Given,

= 506, = 107

We convert this to standard normal as

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

a)

P( X < 600) = P( Z < 600 - 506 / 107)

= P( Z < 0.8785)

= 0.8102

= 81.02%

b)

P( X > 525) = P( Z > 525 - 506 /107)

= P( Z > 0.1776)  

= 1 - P( Z< 0.1776)

= 1 - 0.5705

= 0.4295

Of the 1000 SAT verbal scores we expect, 1000 * 0.4295 = 429.5  

= 430 SAT verbal scores would be greater than 525.