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 tp be admitted tothis 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 what percentage did tom get?

Answer 1

Answer:

Given,

μ=500 (mean) 

σ=100 (standard deviation)

Tom does better than what percentage?

Tom got 585 marks

we will have to find how many students got less than 585

x<585 (find the probability)

converting the problem in standard form

Z=(x−μ)/σ

for x=585

Z=(585−500)/100=0.85

P(Z<0.85)=P(Z<0)+P(0<Z<0.85)

P(Z<0)=0.5

P(0<Z<0.85)=0.3023  (from Z- table)

so the total probability=0.5+0.3023=0.8023

so Tom got more than 80.23% of students