Question

The scores on standardized admissions test are normally distributed with a mean of $500$ and a standard deviation of $100$. What is the probability that a randomly selected student will score between $400$ and $600$ on the test?

• A. About $63\%$
• B. About $65\%$
• C. About $68\%$
• D. About $70\%$

Answer 1

The correct option is C About $68\%$

For normal distribution ,

The scores on standardised admissions test are normally distributed with a mean of 500500

Mean ($\mu$)=500

standard deviation($\sigma$)=100

Probability that score lies between 400 and 600 i.e, P(400<x<600)

For standard normal distribution curve

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

(400-500)/100<(x-$\mu$)/$\sigma$<(600-500)/100

-1<Z<1

For standard normal distribution mean shifted to zero,

Also,P(-1<Z<1)=area of the region between -1 to 1 that is approximately equal to=68%