Question

Using the Empirical Rule for a distribution of widget weights with a mean of 37 ounces and a standard deviation of 7 ounces:

95% of the widget weights lie between _______ and _______.

Answer 1

Approximately 95% of the widget weights, given a mean of 37 ounces and standard deviation of 7 ounces, lie between 23 ounces and 51 ounces according to the Empirical Rule.

Step-by-step explanation:

Using the Empirical Rule, we can determine that approximately 95% of the widget weights lie within two standard deviations of the mean in a normal distribution. Since the mean of the widgets is 37 ounces and the standard deviation is 7 ounces, we calculate the range for 95% of the widget weights as follows:

Lower Bound = Mean - 2(Standard Deviation) = 37 - 2(7) = 37 - 14 = 23 ounces

Upper Bound = Mean + 2(Standard Deviation) = 37 + 2(7) = 37 + 14 = 51 ounces

Therefore, using the Empirical Rule, 95% of the widget weights lie between 23 ounces and 51 ounces.