A random sample of 36 observations is drawn from a population with a mean equal

Question

A random sample of 36 observations is drawn from a population with a mean equal to 65 and a standard deviation equal to 12 a. What is the mean and the standard deviation of the sampling distribution of x7 63 b. Describe the shape of the sampling distribution of x Does this answer depend on the sample size? doesdepend on the sample size The shape is that of a normaldistribution and oes c. Calculate the z-score corresponding to a value of x 62.6. d. Calculate the z-score corresponding to a value of x 69.4. e. Find P(x 2 62.6) (to 4 decimals) f. Find P(x 69.4) (to 4 decimals) g. Find P(62.6 s xs 69.4) (to 4 decimals) (to & decimals). h. There is a 60% chance that the value ofx' is above!

Explanation / Answer

A)

Mu=65

Sigma =12

B)normal,does

C)z=(x-mu)/(sigma/?n)

Z=(62.6-65)*6/12

Z=-1.2

D)z=(69.4-65)/(12/6)

Z=2.2

E)p(x>=62.6)

P(z>=-1.2)

=0.8849

F)p(x<69.4)

P(z<2.2)

0.9861

G)

P(-1.2<z<2.2)

=0.3849+0.4861

=0.871

H)z=-0.26(from table)

Z=(x-mu)/(sigma/?n)

-0.26 =(x-65)/(12/6)

X=63.96

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