Question #2605

Let x represent the life of a 60-watt light bulb. The x distribution has a mean of 1000 hours with standard deviation of 75 hours. Convert each of the following z intervals to x intervals.
(a) z > 1.25
(b) -1.5 > z > 2.4
(c) z > 2.25

Expert's answer

By definition

& z = (x-a)/sigma,

where a=1000 is a mean of x, and sigma = 75 its standard deviation.

Hence

(a)& z> 1.25

means that

(x-1000)/75 > 1.25

x > 1000 + 75 *1.25

x> 1039.25

(b) the inequality

& -1.5& > z& >& 2.4

Is incorrect.

Perhaps here should be

-1.5 < z <& 2.4

Then

1000-1.5*75 < x < 1000+2.4*75

887.5 < x < 1180

(c)& z> 2.25

& x > 1000 + 75 *2.25

x> 1168.75

& z = (x-a)/sigma,

where a=1000 is a mean of x, and sigma = 75 its standard deviation.

Hence

(a)& z> 1.25

means that

(x-1000)/75 > 1.25

x > 1000 + 75 *1.25

x> 1039.25

(b) the inequality

& -1.5& > z& >& 2.4

Is incorrect.

Perhaps here should be

-1.5 < z <& 2.4

Then

1000-1.5*75 < x < 1000+2.4*75

887.5 < x < 1180

(c)& z> 2.25

& x > 1000 + 75 *2.25

x> 1168.75

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