Question

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?

Answer 1

Given that,

mean = = 500

standard deviation = = 100

Using standard normal table,

P(Z > z) = 70%

= 1 - P(Z < z) = 0.70  

= P(Z < z ) = 1 - 0.70

= P(Z < z ) = 0.30

= P(Z < -0.52) = 0.30

z = -0.52

Using z-score formula  

x = z +

x = -0.52 *100+500

x = 448

yes tom score is good than his admitted to this university