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Question

A manufacture produces a commodity where the length of the commodity has approximately normal distribution with a mean of 14.6 inches and standard deviation of 0.7 inches if a sample of 43 items are chosen at random what is the probability the samples mean length is greater than 14.4 inches Round answer to four decimal places

Answer 1

z= (x - mean)/s/sqrN = (14.4-14.6)/.7/sqr43 = -.2/.7/sqr43 = -2sqr43/7 = about -1.87355

where mean = 14.6, N=43, s=standard deviation = .7

use z tables or a z calculator to find the area under the curve to the right of -1.87355 = .9695 rounded to 4 decimal places

= 96.95% probability x>14.4 inches