Question

Questions 1-6 please. ASAP please. will rate, ty.

QUESTION 1 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 96 and a standard deviation of 24. Complete the following statements about the distribution of scores on this personality test. (a) According to Chebyshev's theorem, at least? between 36 and 156 of the scores lie of the scores lie (6) According to Chebyshev's theorem, at least ? between 48 and 144 (C) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of the scores lie between 48 and 144. X 5 ? (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the scores lie between and [.

Answer 1

We would be looking at first question all parts here as:

Q1) We have here:
Mean = 96 and SD = 24 that is mean and standard deviation are given here.

a) The z score for 96 here is computed as:

Z₃₆ = (36 - Mean)/SD = (36 - 96)/24 = -60/24 = -2.5

Z₁₅₆ = (156 - Mean) / SD = (156 - 96) /24 = 2.5

According to chebyshev;s inequality theorem at least 1 - 1/k² of the observations lies within k standard deviation of the mean.

Here k = 2.5

therefore, 1 - 1/k² = 1 - 1/2.5² = 0.84

Therefore 84% is the correct answer here.

b) Similar to above method, we have here:

Z₄₈ = (48 - 96)/24 = -2

Z₁₄₄ = (144 - 96) / 24 = 2

Therefore 1 - 1/2² = 0.75

Therefore 75% is the correct answer here.

c) According to empirical rule, 95% of the observations lies within 2 standard deviations of the mean. Therefore 95% is the correct answer here.

d) According to empirical rule, 68% of the observations lies within 1 standard deviation of the mean. Therefore, the limits here are computed as:

L = Mean - SD = 96 - 24 = 72
U = Mean + SD = 96 + 24 = 120

Therefore 72 and 120 are the required limits here.