The lives of certain extra-life light bulbs are normally distributed with a mean

Question

The lives of certain extra-life light bulbs are normally distributed with a mean equal to 1350 hours and a standard deviation equal to 18 hours. 1. What percentage of bulbs will have a life between 1350 and 1377 hr? 2. What percentage of bulbs will have a life between 1341 and 1350 hr? 3. What percentage of bulbs will have a life between 1338 and 1365 hr? 4. What percentage of bulbs will have a life between 1365 and 1377 hr? 5. What percentage of bulbs will have a life between 1338 and 1344 hr? 6. What percentage of the bulbs will last longer than 1386 hr? 7. What percentage of the bulbs will last less than 1323 hr? 8. The 10 percent of the bulbs with the longest life will last longer than how many hours? 9. The 20 percent of the bulbs with the shortest life will last no longer than how many hours?

Explanation / Answer

(a)

Calculating z-score as:

z = (1377-1350)/18 = 1.5

Using cumulative z-table, the required probability is: 0.93-0.50 = 0.43

(b)

Calculating z-score as:

z = (1341-1350)/18 = -0.5

Using cumulative z-table, the required probability is: 0.50-0.308 = 0.192

(c)

Calculating z-score as:

z = (1365-1350)/18 = 0.833

Using cumulative z-table, the probability for this z-score is: 0.797

At x = 1338,

z = (1338-1350)/18 = -0.67

Using cumulative z-table, the probability for this z-score is: 0.251

So, required probability is: 0.797-0.251 = 0.546

(d)

Calculating z-score as:

z = (1365-1350)/18 = 0.833

Using cumulative z-table, the probability for this z-score is: 0.797

At x = 1377,

z = (1377-1350)/18 = 1.5

Using cumulative z-table, the probability for this z-score is: 0.933

So, required probability is: 0.933-0.797 = 0.136

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