The Acme Company manufactures widgets. The distribution of widget weights is bel

Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 39 ounces and a standard deviation of 6 ounces. Use the Standard Deviation Rule, also known as the Empirical Rule. i&ii) 68.2% of the widget weights lie between Blank 1 and Blank 2. iii) What percentage of the widget weights lie between 21 and 45 ounces? Blank 3 Answer as a whole number. iv) What percentage of the widget weights lie above 27? Blank 4 Answer as a whole number.

Explanation / Answer

mean is 39 and s is 6, z is calculated as (x-mean)/s

a) for 68.2%, the values lie in 1 standard deviation from the mean, thus lower limit is mean-s*z i.e 39-1*6=33

upper limit is 39+1*6=45

b) P(21<x<45) =P((21-39)/6<z<(45-39)/6)=P(-3<z<1) or P(z<1)-P(z<-3) =P(z<1)-(1-P(z<3)) form normal distribution table we get 0.8413-(1-0.9987)=0.84

c) P(x>27)=P(z>(27-39)/6)=P(z>-2) or 1-P(z<2), from normal table we get 1-0.9772=0.0228

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