Question

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 44 ounces and a standard deviation of 10 ounces. Use the Empirical Rule. Suggestion: sketch the distribution in order to answer these questions. a) 95% of the widget weights lie between 34 and 54 b) What percentage of the widget weights lie between 34 and 64 ounces

Answer 1

Answer:

a) No 95% of values will fall between (24;64); 68,27% will fall between (34;54)

b)71,83 % will fall between 34 and 64 ounces

Step-by-step explanation:

Empirical rule establishes, for a  normal distribution with mean μ and σ as standard deviation:

In interval   μ  ±  σ    or   ( μ  +  σ ;  μ  -  σ) we should find 68.27 % of all values of the population, and by simmetry 68.27/2 = 34,14 % should be over the mean and the other half would  be values below the mean

Therefore in our case

μ  +  σ  =  44 + 10  =  54

And

μ  -  σ  = 44 - 10   = 34

a) Then  68,34 % of values will fall in this interval

We know now that value 34 is 1* σ   below the mean, and is at the limit of 34,14 %

b) μ  +  2*σ  =   44 * 2*10  =  44 + 20  =  64

64 is the upper limit for the interval   μ  +  2*σ  and we know that 95.45 % of all values will fall between (  μ  -  2*σ  ;  μ  +  2*σ ) and by simmetry just one side of this interval (the right side ) will have 95.45/2 = 47;73 %

Then in interval going from ( 34 ; 64 ) we shoud find 47.73 + 34,14

71,83 % of all values will fall between 34 and 64