homework. Hw6-Ch6(25) Score: 3.5 of 7 pts Save 20, 5 (5 complete) Hw score: 81.3

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homework. Hw6-Ch6(25) Score: 3.5 of 7 pts Save 20, 5 (5 complete) Hw score: 81.31%, 20.33 of 25 pt 6.2.29 Question Help An index that is a standardized measure used in observing infants over time is Click here to view page 1 of the standard normal table approximately normal with a mean of 110 and a standard deviation of 11. Answer the questions below Click here to view page 2 of the standard normal table a. What proportion of children have an index of (0) at least 121? (i) at least 757 0) The proportion of children having an index of at least 121 is 1587 (Round to four decimal places as needed.) (H) The proportion of children having an index of at least 75 is 9993 (Round to four decimal places as needed.) b. Find the index score that is the 85th percentile. The 85th percentile index score is 121.44 (Round to two decimal places as needed.) c. Find the index score such that only 15% of the population has an index below it. 15% ofth@ population have an index score below[.]. (Round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer

Explanation / Answer

Answer to the question with formulae and calculations:

a.

i) P(X>=121) = P(Z>= 121-110 / 11) = P(Z>=1) = .1587
ii)P(X>=75) = P(Z> = 75-110/11) = P(Z>-3.18) = .9993

b. P(X=c) = .85
Z = 1.035 is Z value for .85 cumulative area.
Hence, c = Z*Sigma+Mean = 1.035*11+110 = 121.39

c. P(X<=c) = .15
So, Z is -1.035
So, c = -1.035*11+110 = 98.62
So, 15% of the population have an index score below 98.62

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