Question

A particular fruit's weights are normally distributed, with a mean of 380 grams and a standard deviation of 35 grams.

If you pick 32 fruits at random, then 12% of the time, their mean weight will be greater than how many grams?

Give your answer to the nearest gram.

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Answer 1

Given,

= 380 , = 35

Using central limit theorem,

P( < x) = P(Z < (x - ) / ( / sqrt(n) ) )

We have to calculate x such that P( > x) = 0.12

That is

P( < x) = 1 - 0.12

P( < x) = 0.88

P(Z < (x - ) / ( / sqrt(n) ) ) = 0.88

From Z table, z-score for the probability of 0.88 is 1.175

(x - ) / ( / sqrt(n) ) = 1.175

(x - 380) / ( 35 / sqrt(32) ) = 1.175

Solve for x

x = 387