Question

Suppose an analyst wants to use the information on commodity prices introduced in an article Commodity- Indexed Debt(Columbia Journal of World Business). These prices have a mean of 75 cents and a standard deviation of 9 cents. A random sample of 81 commodity prices is selected. ar Describe price for samples of 81 commodity b). What is the probability that the mean of the sample wl be larger than 84 cents? c). What is the probability that the mean of the sample will be between 74 and 76 cents? d). Fifteen percent of the prices are less than what sample mean? the sampling distribution of the mean

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Answer #1

a) Let ar{X} denotes the sample mean price for samples of 81 commodity prices.

Here,

92 81 X ~ Ņormal(75,--)or X ~ Normal (75,12)

b) The probability that the mean of the sample will be larger than 84 cents

P(X 84)

X-75 8475 P(

P(Z > 9)

1- P(Z <9)

= 1-4) ( 9 )

= 1 - 1

= 0

c) The probability that the mean of the sample will be between 74 and 76 cents

P(74< X < 76)

P(X < 76)-P(X < 74)

X-75 76-75 P( X-75 74-75

= P(Z leq 1)-P(Z leq -1)

= Phi(1)-Phi(-1)

0.8413450.158655

0,682690

d) To find x such that

P(X < z) = 0.15

Y-75 r- 75 ) = 0.15

T75 ) = 0.15

75

T75 x-í. Ф-1 (0.15)--1.03643

75-1.03643

Rightarrow x = 73.9636 (ans)

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