Sample Distribution help please

[sheed30]

A study of the amounts of time college freshmen study each week found the distribution to be approximately normal with a mean of 7.06 hours and a standard deviation of 5.32 hours.

If 55 freshmen are randomly selected, find the probability that their mean weekly study time exceeds 7.00 hours.

I have no idea where to start. i'm thinking you go

square root of something to get something else. i know all the equations, i just need an idea for what equation i need to use.

 

[sasan]

You must to google a bit.... a found this example on the net... see more details here: http://www.intmath.com/Counting-probability/14_Normal-probability-distribution.php







It was found that the mean length of 100 parts produced by a lathe was 20.05 mm with a standard deviation of 0.02 mm. Find the probability that a part selected at random would have a length
(a) between 20.03 mm and 20.08 mm
(b) between 20.06 mm and 20.07 mm
(c) less than 20.01 mm
(d) greater than 20.09 mm.

Answer

X = length of part
(a) 20.03 is 1 standard deviation below the mean;
20.08 is

standard deviations above the mean

So the probability is 0.7745.
(b) 20.06 is 0.5 standard deviations above the mean;
20.07 is 1 standard deviation above the mean

So the probability is 0.1498.
(c) 20.01 is 2 s.d. below the mean.

So the probability is 0.0228.
(d) 20.09 is 2 s.d. above the mean, so the answer will be the same as (c),

P(X > 20.09) = 0.0228.
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