Question

v31) The weights of a certain variety of cucumbers are normally distributed with a standard deviation of 2 ounces. Given that 15% of these cucumbers weigh more than 16 ounces, what is the mean weight

Answer 1

13.928 ounces

Explanation:

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score = 16 ounces

μ is the population mean = ??

σ is the population standard deviation = 2 ounces

Given that 15% of these cucumbers weigh more than 16 ounces,

= 100 - 15 = 85

We find the z score for a 85th percentile using the percentile table = 1.036

Hence

1.036 = 16 - x/2

Cross Multiply

1.036 × 2 = 16 - x

2.072 = 16 - x

2.072 - 16 = -x

-13.928 = -x

x = 13.928 ounces

Therefore, the mean weight is 13.928 ounces