Answer to Question #2605 in Statistics and Probability for Hannah

Question

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

Answer 1

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