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A particular fruit's weights are normally distributed, with a mean of 331 grams and a standard deviation of 23 grams. If you pick 15 fruits at random, then 14% of the time, their mean weight will be greater than how many grams?

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Answer:

337.41366

Step-by-step explanation:

Given that:

Mean = 331 grams

Standard deviation = 23 grams

Sample size (n) = 15

P(Z < x) = 14% = 0.14

Obtain the Zscore corresponding to (1 - 0.14) = 0.86

P(z < 0.86) = 1.08

Zscore = 1.08

Zscore = (x - mean) / s/√n

1.08 = (x - 331) / 23/sqrt(15)

1.08 = (x - 331) / 5.9385744

X - 331 = 6.4136604

X = 6.4136604 + 331

X = 337.41366

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