Score data from a statewide exam for 10th-graders follows a normal distribution, has a mean of 90 , and has a standard deviation of 7.8. According to the Empirical Rule, 34% of test scores fall into what range? select all that apply Below 82.2

below 82.2 and above 97.8

between 82.2 and 90

below 90

between 90 and 97.8

above 90

above 97.8

Between 82.2 and 90

Between 90 and 97.8

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 90

Standard deviation = 7.8.

According to the Empirical Rule, 34% of test scores fall into what range?

68% of the measures are within 1 standard deviation of the mean.

The normal distribution is symmetric, which means that 68/2 = 34% fall between one standard deviation of the mean and the mean and 34% fall within the mean and one standard deviation above the mean.

90 - 7.8 = 82.2

90 + 7.8 = 97.8

34% between 82.2 and 90

34% between 90 and 97.8

So the correct options are:

Between 82.2 and 90

Between 90 and 97.8

the answer to the expression is 83

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