Question

The weights of bags of pet food are distributed normally about the mean, 50 lb. The standard deviation is 0.2 lb. In a group of 20 bags, about how many would you expect to be within one standard deviation from the mean?

Answer 1

Using the empirical rule for normal distributions, approximately 68% of the data falls within one standard deviation of the mean. Therefore, in a group of 20 bags of pet food with a normal distribution, about 14 bags are expected to be within one standard deviation from the mean.

Step-by-step explanation:

The question involves the concept of a normal distribution in statistics, and specifically, how it applies to the weights of bags of pet food. Given that the bags have a mean weight of 50 lb and a standard deviation of 0.2 lb, we can use the empirical rule (68-95-99.7 rule) for normal distributions. This rule states that approximately 68% of the data in a normal distribution falls within one standard deviation of the mean.

In this scenario, we have a group of 20 bags of pet food. To find out how many bags we would expect to fall within one standard deviation from the mean, we would calculate 68% of 20:

Expected number of bags within one standard deviation = 0.68 × 20 = 13.6

Rounding to the nearest whole number, we can expect about 14 bags to fall within one standard deviation from the mean.

Answer 2

With a normal distribution, we can expect that no more than 5% of the values fall within one standard deviation of the mean. Those in the 5% may have up to 50.02 or 49.98 pounds of pet food.