The author\'s Generic generator produces voltage with a mean of 178.03 volts and

Question

The author's Generic generator produces voltage with a mean of 178.03 volts and standard deviation of 0.08 volt, and the voltages have a bell-shaped distribution using the rule. What is the approximate percentage of voltage amounts between 177.79 volts and 178.27 volts? What is the approximation percentage voltage amounts is less than 177.79 volts? What is the approximation percentage of voltage amounts is move then 178.27 The average 20-to 29-years-old man is 79.9 inches tall, with a standard deviation of 3.1 inches, while the average 20-to 29-years-old woman is 64.1 inches tall, with a standard deviation of 3.8 inches. Who is taller a 74-inch man or a 70-inch woman?

Explanation / Answer

13) here from normal distribution z=(X-mean)/std deviation

a) P(177.79<X<178.27)=P((177.79-178.03)/0.08<Z<(178.27-178.03)/0.08)=P(-3<Z<3) =0.9973 or 99.73%

b)as 177.79 lie 3 std deviation below mean . hence approximate %=((1-0.9973)/2)*100=0.135%

c)similalry178.27 lie 3 std deviation above mean . hence approximate %=((1-0.9973)/2)*100=0.135%

14)z score for 74 inch man =(74-79.9)/3.1=-1.90323

and z score for 70 inch women =(70-64.1)/3.8=1.5526

as z score of women is higher , she is relatively taller.

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