8 Given a normal distribution with 50 and and X 56 is approx

8. Given a normal distribution with -50 and and X- 56 is (approximately) 6, the area under the distribution between x-50 a. .18 b. .34 C. .48 d. .68 9. You analyzed a set of scores and found that R = 10, s-2 , and s2-4 . Your colleague decided to transform the data by adding a 5 to all scores and then multiplying by 2. Without having to reanalyze the data, you were able to compute the new X, s, and . What were X and ? a. X=30, s2=8 b. X-30, s2-16 c, X = 20 , s2=8 d,X=20, s2 = 16 e. X=15, s2=8 For a sample of scores on a personality assessment of Conscientiousness,the mpute the unbiased sample standard deviation of these scores. (a) Provide a formula and ( mean is 5. . ke relevant substitutions. You need NOT do any arithmetic.

Solution

9.

If the old data set has mean Xbar, standard deviation s, and variance s^2, then, if you add 5 on all data, then multiply by 2,

New Mean = 2 (Xbar + 5) = 2(10 + 5) = 30 [answer]
New variance = 2^2 (s^2) = 4s^2 = 4(4) = 16 [answer]

[For the variance, adding any number will not affect it, but multiplying does.]

Hence,

ANSWER: OPTION A: X = 30, s^2 = 16 [answer]