The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 50 ounces and a standard deviation of 10 ounces. Use the Empirical Rule, what percentage of the widget weights lie between 43 and 87 ounces?

The probability of the widget weights lie between 43 and 87 ounces

P(43 ≤ x ≤ 87 ) = 0.7605

The percentage of the widget weights lie between 43 and 87 ounces

P(43 ≤ x ≤ 87 ) = 76 %

Step-by-step explanation:

Step(i):-

Given mean of the Population = 50ounces

Given standard deviation of the Population = 10 ounces

Let 'X' be the random variable in Normal distribution

Given X = 43

Given X = 87

Step(ii):-

The probability of the widget weights lie between 43 and 87 ounces

                       = |A(3.7) + A(-0.7)|  

                       =  |A(3.7) + A(0.7)|   (∵A(-z) = A(z))

                      = 0.4994 + 0.2611

                     =  0.7605

Final -

The probability of the widget weights lie between 43 and 87 ounces

P(43 ≤ x ≤ 87 ) = 0.7605

The percentage of the widget weights lie between 43 and 87 ounces

P(43 ≤ x ≤ 87 ) = 76 %

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: