SOLUTION: A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures.​ Historically, the failure rate for LED light bulbs that t

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Question 1152785: A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures.​ Historically, the failure rate for LED light bulbs that the company manufactures is 8​%. Suppose a random sample of 10 LED light bulbs is selected. Complete parts​ (a) through​ (d) below.
a. What is the probability that none of the LED light bulbs are​ defective?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

This is a binomial problem. Each selection is independent of one another, and a bulb is either defective or it is not defective.

p = 0.08 is the probability of being defective
1-p = 1-0.08 = 0.92 is the probability of not being defective
n = 10 is the sample size

Use the Binomial PDF function

x is a non-negative whole number representing the number of defective bulbs

Plug in n = 10 and p = 0.08






Now plug in x = 0, which will help us find the probability of x = 0 bulbs being defective




B%280%29+=+%28%2810%21%29%2F%280%21%2A10%21%29%29%2A%280.08%29%5E0%2A%280.92%29%5E10

B%280%29+=+%28%2810%21%29%2F%281%2A10%21%29%29%2A%280.08%29%5E0%2A%280.92%29%5E10

B%280%29+=+%28%2810%21%29%2F%2810%21%29%29%2A%280.08%29%5E0%2A%280.92%29%5E10

B%280%29+=+1%2A%280.08%29%5E0%2A%280.92%29%5E10

B%280%29+=+1%2A%280.92%29%5E10

B%280%29+=+%280.92%29%5E10

B%280%29+=+0.434+388+454+223+63 Use your calculator. This value is approximate.

When rounded to 3 decimal places, the approximate answer is 0.434