If the true mean is .9340 with a standard deviation of 0.0020, within what interval will 95 percent of the sample means fall
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 = 384 . . . . initial value required for a recursive definition
part c. the general formula for a geometric sequence is
a[n] = a·r^(n-1)
we have a = 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 = 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
130^2 = 16900
16900*26 = 439400
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D $1.15...1 answer(s) · Mathematics
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