th 146 Online W2018> Assessment ormal Curve and The Central Limit Theorem Timeli

Question

th 146 Online W2018> Assessment ormal Curve and The Central Limit Theorem Timelimit: 2 hours. 1:54:25 rema Show Intro/In A population of values has a normal distribution with -230.4 and 31.3 You intend to draw a random sample of szen 15. Find P61, which is the score separating the bottom 61% scores from, the top 39% scores. Pa (for single values) Find P61, which is the mean separating the bottom 61% means from the top 39% means. P61 (for sample means) Enter your answers as numbers accurate to I decimal place. Answers obtained using exact :-scores or 2-scores rounded to 3 decimal places are accepted Points possibte: 5 This is attempt 1 of 2. Submit Sho worksheetforcent docx ^ worksheetforcent docx ^

Explanation / Answer

Here = 230.4

and = 31.3

P61 we have to calculate . Let say it is c

HEre as per Z - table, value of Z for 61 % percentile is Z = 0.2793

so (c - 230.4)/31.3 = 0.2793

c = 230.4 + 31.3 * 0.2793 = 239.143

(ii) Now sample size n = 15

Standard error of sample mean = 31.3/ sqrt(15) = 8.0816

so if sample mean of 61% tile is k

then

(k - 230.4)/8.0816 = 0.2793

k = 230.4 + 8.0816 * 0.2793 = 232.657

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