Statistics Help

Question

500 people were surveyed about the cost of their utility bills.

The mean cost was $125
The standard deviation is $10

What is the number of people who have a utility bill between $105 and $135?

What percentage of people have a utility bill over $145?

How would I solve this problem? I have the information where n= 500, mean is $125, and standard deviation is $10. I've plugged these numbers into my calculator and I drew a bell curve but I am still confused.

Answer 1

I don't know what level you're studying statistics at or what normal curve diagram you're looking at so it's a little hard to give you advice.

 

Your mean is 125. The score of 105 is 20 less than the mean or 2 standard deviations from the mean. According to the tables, 2 SDs from the mean encompasses 47.72% of the population.

 

The score of 135 is 1 standard deviation from the mean. That encompasses 34.13% of the people.

 

So the percent of people in the range 105-135 would be 47.72% + 34.13% = 81.85% of the population.

 

So 81.85% of 500 = 409 people.

 

For the second question, What % is over 145....which is 20 above the mean or 2 SDs. According to the normal curve table or graph, 2 SDs above the mean contains 47.72% and below the mean is 50%, so all the scores <= 145 is 97.72%. That means that the remaining 2.28% is > 145.

 

Hope this was of some help.