6 Suppose a simple random sample of size n 64 is obtained f

6) Suppose a simple random sample of size n = 64 is obtained from a population with the u = 73 and o = 32.

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

A) The distribution is approximately normal.

B) The distribution is skewed right.

C) The distribution is unifrom.

D) The distribution is skewed left.

E) The shape of the distribution is unknown

b) Find the mean and standard deviation of the sampling distribution of x

Ux = _

Ox = _

c) P (x > 80.8) = _

d) P (x less than or equal to 63.4) = _

e) P (69.2 < X < 81.8) = _

Round all answers to four decimal places as needed

Solution

(a)A) The distribution is approximately normal.

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(b)

Ux = 73 (stay the same)

Ox = s/vn =32/sqrt(64) =4

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(c)P (x > 80.8) = P((X-mean)/s >(80.8-73)/4)

=P(Z>1.95) =0.0256 (from standard normal table)

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(d)P (x less than or equal to 63.4) = P(X<=63.4)

=P(Z<(63.4-73)/4)

=P(Z<-2.4) =0.0082 (from standard normal table)

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(e)P (69.2 < X < 81.8) = P((69.2-73)/4<Z<(81.8-73)/4)

=P(-0.95<Z<2.2) =0.8150 (from standard normal table)