Question

A particular fruit's weights are normally distributed, with a mean of 740 grams and a standard deviation of 9 grams.

If you pick 19 fruits at random, then 11% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

Answer 1

io we - 11 % 11% = 0,1) 100 Solution :> given, Mean x 740 grams Standard deviation o = 9 grams Sample Size n =19 We take random Variable x as weight of fruit's. o we have to find value of a such that 11% of the time their mean weight will be weight will be greates than X=2 grams have p(xxx) => p (x7,x) = 0,11 os given distribution is noumal. so we find value of z tou p(x>x) =0.11. P(x>) - P(x27) - 0.11 " Using to table, value of a forp (x >,2)=0.11 is. 1. 227. below formula for finding . X-X own -> lo 227 = x - 740 Voir we use OD » Z- P(x>2) =0.ll. z = 1,227 lo 227 = X - 740 2.065 1.297x2.065 = X-740 -> -> 2.5337 = X-740 740 + 2,5337 X = 742.5337. Required weight 742.5337 gram OD

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