Answer to Question #200069 in Statistics and Probability for Sheron

Question

The scores of high school students on a national mathematics exam in SA were normally distributed with a mean of 86 and a standard deviation of 4. If there were 97680 students with scores higher than 91. how many students took the test? 394400 125000 247667 No correct answer provided 925000 105000

Answer 1

Given,

$\mu=86\\\sigma=4\\$

So,

$z=\dfrac{91-\mu}{\sigma}=\dfrac{91-86}{4}=1.25$

So, $P(X>91)=P(z>1.25)$

From table:

$P(z>1.25)=0.1056$

and suppose 'n' students appear in the test.

So, according to question

$n\times 0.1056=97680\\\Rightarrow n=\dfrac{97680}{0.1056}=965000$

Hence, 965000 students appear in the test.