Probability--URGENT!!!!!!!
Message posted by Michelle (via 140.209.34.185) on November 11, 2001 at 7:28 PM (ET)

Here is my problem; I'm told it's supposed to be easy, but I must be overthinking it:
"A standardized test was given to all public school sixth graders in a certain large city. The mean score was 39.6. Assume the standard deviation was 7.
What is the probability that 36 students will have an average score between 36 and 42?"
I would very very much appreciate any insight to this problem. I need an answer by tomorrow at 10 a.m., so hopefully someone out there can help!
Thanks!

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Re: Probability--URGENT!!!!!!!
Message posted by Tomi (via 154.32.143.194) on November 11, 2001 at 8:12 PM (ET)

The theory behind this is that if X~N(mu, sigma^2), then the mean of n values of X, Xbar~N(mu, sigma^2/n). What this means for your problem is that the mean has a standard deviation equal to 7/sqrt(36) = 7/6.

So you have Xbar~N(39.6, 1.167) and you want P(36An important question at this stage is about continuity: can you get only whole number scores or are the scores continuous. I'm assuming that they are discrete (whole number values only).

This means we must apply a continuity correction and calculate P(35.5= P(Xbar<42.5) - P(Xbar<35.5) = P(Z<(42.5-39.6)/1.167) - P(Z<(35.5-39.6)/1.167) = 0.9935 - 0.0002 = 0.9933 or 99%.