Jonathan, a college business student wants to study how many pages of notes fellow classmates took during a semester for a finance class. Past data reveals that pages of notes for a finance college class has a mean of 95 , with standard deviation 25 pages. He plans to take a random sample of 30 such college students and will calculate the mean pages of notes they take to compare to the known pages of notes students take for a finance college class. For these values, the mean and standard deviation of the sampling distribution of sample means for a sample of size 30 are: μx¯=95 and σx¯=2530√=4.6. What is the probability that the sample mean for a sample of size 30 will be at least 99? You may use a calculator or the portion of the z-table given below.

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answer: the first graph

step-by-step explanation:

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