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dsp73
3 years ago
7

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.

Mathematics
1 answer:
daser333 [38]3 years ago
6 0

9514 1404 393

Answer:

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

Step-by-step 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.

__

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.

__

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.

_____

<em>Additional comment</em>

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.)

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