z distribution problem: number of hamburgers consumed

[lulu]

Here's another practice problem I'm working on today. The content is silly, I know... :wink:

Given the average number of hamburgers consumed in Texas during the month of April is 3.5, and the standard deviation is 0.8. Assuming consumption is distributed normally:

a) what percentage of the time does the amount of hamburgers eaten in April exceed 5?
b) a month is classified as "a good month" if amount of hamburgers consumed is in the upper 10% for that month. How many hamburgers must be consumed before a month is classified as "a good month"

So, to try to tackle a), I thought I needed to find the probability of P (x>5). Going to the z distribution table, I came up with P (x>1.875). Then I thought that I needed to do: 1 - .9696, coming up with an answer of .0304. It isn't the right answer, but I'm not sure what I did wrong.

To try to tackle b), I thought the question is asking P(x >= 3.15), because 10% of 3.5 is .35, subtracted from 3.5 gives you 3.15. So, looking up the corresponding z value, I got P (z >= .4375). Then I thought I needed to do: 1 - .165 = .835, which is also not the right answer.

What I am doing wrong? Any thoughts?

 

[tkhunny]

Re: z distribution problem

So, to try to tackle a), I thought I needed to find the probability of P (x>5). Going to the z distribution table, I came up with P (x>1.875).

If you moved to "z", why is it still 'x'? You are on the right track. Why do you think this is not the correct response? Mostly, I do not understand the question. 3½ burgers in a month? There is a bit of a units problem, at least.

 

[lulu]

Sorry, I typed 'x' instead of 'z' in my post.

I know, the units and content seem silly to me. Who would believe Texans consume only 3.5 hamburgers per month. Isn't that cattle country? :wink:

Anyway, I'll take another look at it. According to my teacher, my answers are wrong, although she hasn't seen fit to illuminate me further. I guess that's why I was looking for an independent opinion