Question

A particular fruit's weights are normally distributed, with a mean of 312 grams and a standard deviation of 34 grams. If you pick 7 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.

Answer 1

Solution :

Given that,

mean = = 312

standard deviation = = 34

n = 7

= 312

= / n = 34 / 7 = 12.8508

Using standard normal table ,  

P(Z > z) = 12%

1 - P(Z < z) = 0.12

P(Z < z) = 1 - 0.12

P(Z < 1.18) = 0.88

z = 1.18

Using z-score formula,  

= z * +   = 1.18 * 12.8508 + 312 = 327

327gram