A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall above10.95 ounces.

Question

Mathematics

Figaro

3 November, 23:17

A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall above10.95 ounces.

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Steven Mcmahon · Answer 1

6.68 %.

Step-by-step explanation:

The standardised z-score = (10.95 - 10.5) / 0.3

= 1.5.

Looking up the Normal Distribution tables (area to the left) 1.5 corresponds to 0.93319 so for a weight above 10.95 the proportion is

1 - 0.93319 = 0.06681

= 6.68%.