normal distribtuion

Question

he amount of money that a student at harvard university carries on his/her person is normally distributed with a mean of $25 and a standard deviation of $5. What is the probability that a randomly selected harvard university student will have more than $10 on his/her person? Round to 4th decimal place

Answer 1

Nicole,

 

We have μ = 25 and σ = 5

 

We need to calculate z = (x-μ)/σ

z = (10-25)/5 = -3.00

 

If we look this up on a normal table, we get 0.0013.  But this represents the percent of people who would have at most $10. 

 

To find the percent of students who would have more than $10 on them, we need the complement,

1.0000 - 0.0013 = 0.9987

 

The probability that a randomly selected student has at least $10 is 0.9987 or 99.87%.