Question

A particular fruit's weights are normally distributed, with a mean of 496 grams and a standard deviation of 40 grams. If you pick 32 fruits at random, then 20% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

Answer #1

Solution :

Given that,

mean = = 496

standard deviation = = 40

n = 32

_{}
= 496

_{}
=
/
n = 40 /
32 = 7.0711

P(Z > z) = 20%

1 - P(Z < z) = 0.20

P(Z < z) = 0.20

P(Z < -0.84) = 0.20

z = -0.84

= z *
_{}+
_{}

= -0.84 * 7.0711 + 496 = 490.06

Answer = 490 grams

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