Question

The lifetime of a certain light bulb can be standardized to a Normal model, with a mean of 600 hours and a standard deviation of 55 hours. For a group of 4,800 lights use the Empirical Rule to determine how many of them are expected to last between 545 hours and 710 hours? The number of lights expected to last between 545 h and 710 h is: (Provide your answer as a whole number)

Answer 1

mean = 600

sd = 55

Approx. 68% of the data lies between ± 1 SD, or between 545 and 655

Approx. 95% of the data lies between ± 2 SD, or between 490 and 710

Approx. 99.7% of the data lies between ± 3 SD, or between 435 and 765

P( 545 < x < 710)

% data that lies between 545 to 600 = 34%

% data that lies between 600 to 710 = 47.5%

P( 545 < x < 710) = 81.5 %

Total no of bulbs = 4800

No of lights = 4800 * 81.5% = 3912

ANS: 3912