Question

Due Tue 12/10/2019 11:59 pm tempt for each question so double check all of your answers before submitting them. 20 The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 41 ounces and a standard deviation of 7 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 99.7% of the widget weights lie between and I b) What percentage of the widget weights lie between 27 and 62 ounces? c) What percentage of the widget weights lie above 34 ? | Points possible: 1 This is attempt 1 of 3 Submit 5:19 PM 12/9/2015 DOLL

Answer 1

Solution :

Given that,

Using Empirical rule,

P($\mu$ - 1$\sigma$< X < $\mu$ + 1$\sigma$) = 68%

P($\mu$ - 2$\sigma$< X < $\mu$ + 2$\sigma$) = 95%

P($\mu$ - 3$\sigma$< X < $\mu$ + 3$\sigma$) = 99.7%

(a)

P(41 - 3 * 7 < X < 41 + 3 * 7) = 99.7%

P(20 < X < 62) = 99.7%

between 20 and 62

(b)

P(27 < X < 62) = P(X < 62) - P(X < 27) = 0.9985 - 0.025 = 97.35%

(c)

P(X > 34) = 1 - P(X < 34) = 1 - 0.16 = 84%