A particular type of plastic soap bottle is designed to have a capacity of 15 ounces. There is variation in the bottle manufacturing process. Based on historical data, suppose the bottle capacity can be reasonably modeled by a normal distribution with a mean of 15 ounces and a standard deviation of 0.2 ounces. What proportion of these bottles will have a capacity between 14.7 and 15.1 ounces

Question

Lorelei Vincent

Mathematics

7 April, 02:21

A particular type of plastic soap bottle is designed to have a capacity of 15 ounces. There is variation in the bottle manufacturing process. Based on historical data, suppose the bottle capacity can be reasonably modeled by a normal distribution with a mean of 15 ounces and a standard deviation of 0.2 ounces. What proportion of these bottles will have a capacity between 14.7 and 15.1 ounces

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Michelle · Answer 1

62.73%

Step-by-step explanation:

The mean of the data is 15 and the standard deviation is 0.2. The range of data we want is 14.7 - 15.1. We need to change the range into mean + / - SD. The bottom range is 14.7, its lower than the mean (15) by 0.3, so it's mean - 1.5SD. The top limit is 15.1 which higher than 15 by 0.1, so it's mean + 0.5 SD.

The range of data we want is - 1.5 SD to + 0.5 SD

The z-score for - 1.5 is 0.06681 and the z-score for + 0.5 SD is 0.69416. The proportion will be 0.69416-0.06681 = 0.62735 = 62.73%