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 3 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule.

Suggestion: sketch the 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 43 and 87 ounces?

c. What percentage of the widget weights lie below 76 ?

(a) 68% of the widget weights lie between 43 ounces and 49 ounces.

(b) The percentage of the widget weights lie between 43 and 87 ounces is 15.87%.

(c) The percentage of the widget weights lie below 76 is 100%.

Step-by-step explanation:

Let X = weight of widgets manufactured by Acme Company.

The distribution of the random variable X is, N (μ = 46, σ² = 3²).

According to the Empirical Rule in a normal distribution with mean µ and standard deviation σ, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be broken into three parts:

(a)

According to the Empirical rule, 68% data falls within 1 standard deviation of the mean.

P (µ - σ ≤ X ≤ µ + σ) = 0.68.

Compute the upper and lower values as follows:

µ - σ = 46 - 3 = 43 ounces

µ + σ = 46 + 3 = 49 ounces

Thus, 68% of the widget weights lie between 43 ounces and 49 ounces.

(b)

Compute the probability of the widget weights lie between 43 and 87 ounces as follows:

*Use a z-table.

The percentage is, 0.1587 × 100 = 15.87%.

Thus, the percentage of the widget weights lie between 43 and 87 ounces is 15.87%.

(c)

Compute the probability of the widget weights lie below 76 as follows:

*Use a z-table.

The percentage is, 1 × 100 = 100%.

Thus, the percentage of the widget weights lie below 76 is 100%.

i think 1: 2

step-by-step explanation:

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.