Question

A particular fruit's weights are normally distributed, with a mean of 486 grams and a standard deviation of 16 grams.

If you pick 11 fruits at random, then 10% 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 = = 486

standard deviation = = 16

n = 11

= = 486 and

= / n = 16 / 11 = 4.8242

P( Z > z ) = 10%

1 - P( Z < z ) = 0.10

P( Z <  ) = 1 - 0.10

P( Z < z ) = 0.90

P( Z < 1.28) = 0.90

z = 1.28

Using z - score formula,

X = z *   +

= 1.28 * 4.8242 + 486

= 492

Their mean weight will be greater than 492 grams.