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 $585$. Tom does better than what percentage of students?

• A. $89.23$%
• B. $77.26$%
• C. $70.23$%
• D. $80.23$%

Answer 1

Answer: (D)

$80.23$%

Given,

$\mu =500$ (mean)

$\sigma =100$ (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

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

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