Statistic Help- Any Stats genius'' here?

[iwannaprettyone]

This is the only question I missed on my midterm and I can''t understand why, anyone know how to work this???


An accounting firm is planning for the next tax preparation season. From last year''s returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.
What is the probability that the mean completion time will be more than 120 minutes?

 

[FrekeChild]

IWPO, If no one answers by the time FF gets back into town, I''ll have him look at it. I totally suck at stats, but he tutored it for 3 years, teaches stats for social science, and was (and depending on the day, still is) pursuing a MA in stats. K?

 

[iwannaprettyone]

Thanks dear! I know I am missing something completely ridicolous, but I think I have looked at it for too long and now my brain is boggled! (or pickled haha)

 

[FrekeChild]

Lol! Oh I know what you mean! I have a stats exam later today, and I''m afraid I''m not going to do well on it at all, and your question isn''t making any sense to me right now! Which is probably a very bad sign! How I wish he had been home to help me out last night...

 

[kama_s]

Is the data normally distributed? If it is, you can use normal distribution statistics to find out the probability, given that 68.3% will fall between the +/-1 of the SD.

 

[partgypsy]

Yes, can you just look under the area of the curve to see what the normal distribution is at that point (around 16% or so?). It''s been awhile since I''ve had to calculate anything like that by hand.

 

[iwannaprettyone]

OHHHHH I see!

I got it, thank you soo much.

 

[FrekeChild]

I see you''ve already gotten help, but I emailed your post to him, and since he wrote me back I figure I''ll post it anyway...

it''s something like this (have to run, so you should tell her to check my work)

x = prep time for a tax filing

mu (last year) = 90 = average prep time for the 100 selected filings
std. dev (last year) is 140

question is: what is probability that mean-filing time > 120... or p(mu>120)

because the sample size is 100, we can use central limit theorem to
approximate this normally

p(z > (120-90)/(140/sqrt(100))
= p ( z > 30/14)
= p ( z > 2.14ish)

using a z-table, we can find that probability to be .1271 (have to be
careful with the z-table here, as you are looking for the probability
of something greater than, so the right tail of the curve)