Question

1. 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 5%. Suppose a random sample of  n = 10 LED light bulbs is selected.

1. Based on this data in table of part a, compute the expected value of the number of defective LED light bulbs out of 10 selected bulbs (the mean of the distribution).
2. Based on this data in table of part a, compute the variance and standard deviation of the number of defective LED light bulbs out of 10 selected bulbs (the mean of the distribution).
3. Create a complete probability table (using excel), tabulating all possible cumulative probability values?

x	P(Xx)
0
1
…
n

Answer 1

Here p=0.05 is same for all, n=10 is constant, events are independent only two outcomes

Hence all properties of binomial are satisfied

a. Mean value is

b. Variance is

So Standard deviation is

c.

x	P(x)=BINOMDIST(x,n,p,0)
0	0.5987
1	0.3151
2	0.0746
3	0.0105
4	0.0010
5	0.0001
6	0.0000
7	0.0000
8	0.0000
9	0.0000
10	0.0000