Suppose that at Northside High, the number of hours per week that seniors spend on homework is approximately Normally distributed with a mean of 18.6 and a standard deviation of 6. We take a random sample of 36 seniors. What is the mean and standard deviation of the sampling distribution for the 36 students?

The mean and standard deviation of the sampling distribution for the 36 students will be:

Mean = 18.6

Standard deviation = 6

Step-by-step explanation:

The mean and standard deviation of the sampling distribution is equal to the population mean and standard deviation respectively.  The only difference is that the population mean and standard deviation are parameters or fixed values calculated from every individual in the population, while the sample mean and standard deviation are statistics.  Statistics are calculated from only some of the individuals in a population.  They are meant to represent or approximate the population parameters.

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