SunLight Company is planning to manufacture a new lightbulb with an estimated me

Question

SunLight Company is planning to manufacture a new lightbulb with an estimated mean lifetime run of 36,500 hours. Management also believes that the standard deviation is 5,000 hours, and that the lifetime hours are normally distributed.

1.Use Excel to simulate the hours obtained from a sample of 500 lightbulbs, and use the COUNTIF function to determine the number of bulbs that last longer than 40,000 hours. What is your estimate of the percentage of bulbs that will exceed 40,000 hours?

2. Use COUNTIF to find the number of lightbulbs expected to last fewer than 32,000 hours. Then, find the number with fewer than 30,000 hours and the number with fewer than 28,000 hours.

3.If management would like to advertise a light bulb guarantee such that approximately no more than 10% of the bulbs would last long enough to qualify for the guarantee, what is your recommendation as far as the life of the lightbulbs, in hours, that should qualify for the guarantee?

Please answer in essay format, showing work.

Explanation / Answer

In excel by using formula = NORMINV (RAND(), 36500, 4000)  , i have taken 500 samples.

(1) Out of 500 samples, number of bulbs that last longer than 40,000 hours = 134

It is calculated by using COUNTIF functio.

Estiamted of percenage of bulbs lifetime greater than 40,000 units = 134/ 500 = 0.268

(2) Number of credit out of 500 counts, last fewer than 32,000 hours = 63

Number of credit out of 500 counts, last fewer than 30,000 hours = 30

Number of credit out of 500 counts, last fewer than 28,000 hours = 13

(3) We will calculate it both methods:

(a) Simulation method : where 10 % or say 50 of the bulbswould last long enough to qualify for the guarantee.

that means lifetime value of 450th bulb if simulation sample is arranged in ascending order.

That value is = 42901

(b) Normal probability method

Pr(X >x ; 36500; 4000) = 0.1

so from Z - table

Z = 1.28

(x - 36500)/ 4000 = 1.28

x = 36500 + 4000 * 1.28 = 42620 hours

so About 42900 hours must be given the warrenty time.

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