Question

State administered standardized reading exam is given to eighth grade students. The scores on this exam for all students statewide have a normal distribution with a mean of 536 and a standard deviation of 70. A local Junior High principal has decided to give an award to any student who scores in the top 10% of statewide scores.

How high should a student score be to win this award?

Give your answer to the nearest integer. For help on how to input a numeric answer, please see the instructions for entering numeric response.

Please explain

Answer 1

Given that, mean $(\mu)$ = 536 and

standard deviation $(\sigma)$ = 70

We want to find, the value of x such that, P(X > x) = 0.10

$P(X > x) = 0.10$

$=> 1 -P(X < x) = 0.10$

$=> P(X < x) = 0.90$

$=> P(\frac { X -\mu}{\sigma} <\frac { x - 536}{70}) = 0.90$

$=> P(Z <\frac { x - 536}{70}) = 0.90$

$=> \frac { x - 536}{70}= Z_{0.90}$

$=> \frac { x - 536}{70}= 1.28$

$=> x =( 1.28*70) &plus; 536$

$=> x = 89.6&plus; 536$

$=> x = 625.6$

$=> x \approx 626$

Therefore, student should score 626 to win this award.