Store A sells melons that weigh 22 pounds on average with a standard deviation of 2.5. Store B sells melons that weigh 18 pounds on average with a standard deviation 2 pounds. You take an SRS of 40
melons from store A and an SRS of 34 from store B.
(A) Find the mean of each sampling distribution.
(B) Would it be reasonable to use the standard deviation formula? Explain.
(C) Find standard deviation of each sampling distribution.
(D) How would you describe each distribution?
(E) How would you describe the distribution of difference in mean weight of samples from the two
stores?
(F) Find the mean and standard deviation of the difference in the weight of melons from stores A and B.
(G) How frequently do the mean weights of the melons exceed 5 pounds?

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1

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