A new extended-life light bulb has an average life of 750 hours, with a standard

Question

A new extended-life light bulb has an average life of 750 hours, with a standard deviation of 50 hours. If the life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours? 8. The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68% of the incomes lie between what two incomes? 9. 10. A large manufacturing firm tests job applicants. Test scores are normally distributed with a mean of 500 and a standard deviation of 50. Management is considering placing a new hire in an upper-level management position if the person scores in the upper sixth percent of the distribution. What is the lowest score a new hire must earn to qualify for a responsible position?

Explanation / Answer

Solution:-

8. Given information : mean = 750 , Standard deviation : 50

P(600 < X < 900) = P((600 - 750)/50 < (X- µ) / ? < (900 - 750)/50 )
= P(-3 < Z < 3)
= 0.9974
= 99.74%

9. Given mean = 37200 , standard deviation = 800

=> 68% of the incomes lies between two incomes : mean -/+ 1* standard
: 37200 - 800 , 37200 + 800
: 36400 , 38000

10. x = µ + Z*?
x = 500 + 1.55 * 50 = 577.7387 = 578(rounded)

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