Suppose a simple random sample of size n64 is obtained from

Suppose a simple random sample of size n=64 is obtained from a population with u = 70 and o = 8.

(A) Choose the correct description of the shape of the sampling distribution of x.

a) The distribution is approximetly normal.

b) The distribution is skewed left.

c) The distribiution is uniform

d) The distribution is skewed right.

e) The shape of the distribution is unknown.

B) Find the mean and standard deviation of the sampling distribution of x.

ux = _

ox = _

What is P (x > 71)?

What is P (x < 67.75)?

What is P (69.3 <x<71.95)?

(A) a) The distribution is approximetly normal.

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(B)

ux = 70_

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ox = o/vn = 8/sqrt(64) =1_

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What is P (x > 71)?

P(X>71) = P((X-mean)/(s/vn) >(71-70)/1)

=P(Z>1) = 0.1587 (from standard normal table)

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What is P (x < 67.75)?

P(X<67.75) = P(Z<(67.75-70)/1)

=P(Z<-2.25) = 0.0122 (from standard normal table)

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What is P (69.3 <x<71.95)?

P (69.3 <x<71.95)

=P((69.3 -70)/1 <Z< (71.95-70)/1)

=P(-0.7<Z<1.95)

=0.7324 (from standard normal table)