Question

The X-Colour Lab in Los Angeles attempts to produce pictures with a 98% success rate. To check on the quality control, a sample of 500 pictures has been selected. The distribution is assumed to be binomial.

What is the expected number of defective pictures in the sample?

What is the standard deviation of the distribution?

What is the probability of finding between 7 and 13 defectives in the sample if the defective level is 2%?

Answer 1

The distribution given here is:

a) The expected number of defective samples here is computed as:

= n(1-p) = 500*0.02 = 10

Therefore 10 is the expected number of defectives.

b) The standard deviation of the distribution is computed as:

c) The number of defectives could be approximated by a normal distribution such that:

Now the required probability here is:

P( 7 < X < 13 )

Converting this to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.6621 is the required probability here.