1. Given a test that is normally distributed with a mean of 30 anda standard dev

Question

1. Given a test that is normally distributed with a mean of 30 anda standard deviation of 6,

(a) What is the probability that a single score drawnat random will be greater than34?
(b) What is the probability thata sample of 9 scores will have a mean greater than34?
(c) What is the probability thatthe mean of a sample of 16 scores will be either less than 28 orgreater than 32?

Explanation / Answer

=30 =6 a) P(X>34) P(Z>(X-)/)=P(Z>(34-30)/6)=P(Z>0.67) =1-0.7486=0.2514 b) n = 9 so standard error, e = / n = 6/3=2 P(X>34) P(Z>(X-)/e)=P(Z>(34-30)/2)=P(Z>2) =1-0.9772=0.0228 c) n = 16 so standard error, e = / n = 6/4= 1.5 P(X

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