There are dozens of personality tests available on the World Wide Web. One test, scored on a scale of 0 to 200, is designed to give an indication of how "personable" the test taker is, with higher scores indicating more "personability." Suppose that scores on this test have a mean of 103 and a standard deviation of 20. Complete the following statements about the distribution of scores on this personality test. (a) According to Chebyshev's theorem, at least 36% of the scores lie between x and x. (Round your answer to the nearest integer.)
(b) According to Chebyshev's theorem, at least 56% or 75% or 84% or 89% of the scores lie between 63 and 143 .
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% or 75% or 95% or 99.7% of the scores lie between 63 and 143 .
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the scores lie between x and x.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

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

answer: can you show the options ?

step-by-step explanation:

the answer is -1 1/5, also a

hope i

-lavira : )