The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 46 ounces and a standard deviation of 11 ounces.

Use the Empirical Rule and a sketch of the normal distribution in order to answer these questions.

a) 68% of the widget weights lie between__and_

b) What percentage of the widget weights lie between 24 and 57 ounces?

c) What percentage of the widget weights lie below 79

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joaobezerra joaobezerra · Answer 1 · 2022-07-23T00:08:06+02:00

Using the Empirical Rule, it is found that:

a) 68% of the widget weights lie between 35 and 57.

b) The percentage is 81.5%.

c) The percentage is 99.85%.

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

For this problem, we have that:

In item a, 68% of the widgets are within 1 standard deviation of the mean, hence between 35 and 57.

In item b, between 2 standard deviations below the mean(95% of 50% due to the symmetry of the normal distribution) and 1 above(68% of 50%), hence the percentage is: P 34% + 47.5% = 81.5%.

For item 3, below 3 standard deviations above the mean, hence removes only the top 0.15%, hence 99.85%.

More can be learned about the Empirical Rule at https://brainly.com/question/4079902

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