The scores on a school wide test are normally distributed wi

The scores on a school wide test are normally distributed with a mean of 83 and a standard deviation of 5.

What is the probibilty that the mean score in a class of 9 students exceeds 85?
0.3849
0.1554
0.1151
0.3446

In a class of 9 stdents what is the probability a person scores between 78 and 87?
0.4313
0.3706
0.6294
0.2881

So the probibilty that the mean score in a class of 9 students exceeds 85 is

P(xbar>85) = P((xbar-mean)/(s/vn) >(85-83)/(5/sqrt(9)))

=P(Z>1.2) = 0.1151 (from standard normal table)

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So the probability a person scores between 78 and 87 is

P(78<X<87) = P((78-83)/5 <(X-mean)/s <(87-83)/5)

=P(-1<Z<0.8) = 0.6294 (from standard normal table)