Question

28. SAT Scores the average national SAT score is 1019.

If we assume a bell-shaped distribution and a standard deviation equal to 110, what percentage of scores will you expect to fall above 1129? Above 799?

Source: New York Times Almanac.

28^th Question Solution: 16%; 97.5%

For above 1129: 16%

For above 799: 97.5%

Why? please someone send me from where 16% and 97.5% came from?

Answer 1

Solution:-

Let X: National SAT score

X~bell shaped distribution

That means

X~Normal distribution with mean or average= 1019 and standard deviation = 110

Q1)What percentage of score will you expect to fall above 1129?

----->

That is, here we have to find out the probability

P(X>1129) =?

P(X>1129) = 1- P(X<=1129)

By using Excel, the above probability can be calculated as

It gives value

P(X>1129) = 0.158655254

P(X>1129) = 0.16 ----(rounded to 2 decimal)

That is,

P(X>1129) = 16%

(By Converting probability to percentage)

Q2)What percentage of score will you expect to fall above 799?

----->

That is, here we have to find out the probability

P(X>799) =?

P(X>799) = 1- P(X<=799)

By using Excel, the above probability can be calculated as

It gives value

P(X>799) = 0.977249868

P​​​​​(X>799) = 0.977 ----(rounded to 3 decimal)

That is,

P(X>799) = 97.7%

(By converting probability to percentage)

Note:-

For normal distribution, the probability P (X<=x) can be calculated by using Excel as