Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Tom takes the test and scores 585. Will he be admitted to this university?

\$Z = (X-\mu )/ \sigma\$

From the given data

\$\mu = 500 , \sigma = 100 , X = 585\$

Tom got 585 marks,we have to find how many students got less than 585

P(X<585)

Converting to standard normal curve

\$P(X<585) = P((X-\mu )/ \sigma) < (585-500)/100)\$

\$P(X<585) = P(Z<0.85)\$

P(Z<0.85)

(area from 0 to 0.85)

Take the values from the standard normal distribution table or chart

P(Z<0.85)

0.8023

Proportion P of students who scored below 585

0.8023

Tom scored better than 80.23% of the students who took the test and he will be admitted to this university.

Answer

A