Question

The actual weights of bags of pet food are normally distributed about the mean of 50.0 lb with a standard deviation of 0.2 lb.

1. About what percentage of bags of pet food weigh between 49.8 lb and 50.2 lb?

2. About what percentage of bags weigh less than 49.8 lb?

3. In a group of 250 bags, what percentage of bags would you expect to weigh more than 50.4? ​

Answer 1

9514 1404 393

Answer:

1. 68%
2. 16%
3. 2.5%

Explanation:

1. The empirical rule tells you 68% of the distribution is within 1 standard deviation of the mean. The mean is 50 and the standard deviation is 0.2, so this means 68% of the bags weigh between 49.8 and 50.2 lb.

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2. The other 32% is evenly split above and below the central part of the distribution. That is, about 16% of the bags will weigh less than 49.8 lb.

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3. The percentage is independent of the size of the group. The empirical rule tells you 95% lie within 2 standard deviations of the mean. The other 5% will be evenly split between those weighing more than 50.4 and those weighing less than 49.6 lb. About 2.5% of the bags will weigh more than 50.4 lb.

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Additional comment

It is useful to remember the empirical rule numbers, 68%, 95%, 99.7% for the portion of the distribution between ±1, 2, 3 standard deviations of the mean. They are useful for answering questions like this one. (They are only approximations, so if more accuracy is needed, a table or app should be used to find the accurate value.)