Suppose that, based on a sample, the 99.7% confidence interval for the mean of a population is (14, 44). what is the value of s/√n

Population mean = (14,44)
Z at 99.7% = 2.96

Therefore,
Sample mean = (14+44)/2 = 29

However,
Population mean = Sample mean +/- Z*s/Sqrt (n)

Taking one of the ranges, say lower range:
14 = 29-Z*s/Sqrt (n)
14-29 = - 2.96*s/Sqrt (n)
-15 = -2.96*s/Sqrt (n)
5 = s/Sqrt (n)

Therefore,

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a. geometricb. g[h] = (3/4)·g[h-1]; g[1] = 384c. g[h] = 384·(3/4)^(h-1)d. g[12] ≈ 16.2183 gallonse. g[12] ≈ 64.8732 quarts

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