Author Question: Under what conditions is the binomial distribution symmetric? What will be an ideal ... (Read 68 times)

audie · **on:** Jun 24, 2018

Under what conditions is the binomial distribution symmetric?

What will be an ideal response?

Question 2

The Swanson Auto Body business repaints cars that have been in an accident or which are in need of a new paint job. Its quality standards call for an average of 1.2 paint defects per door panel.

Explain why there is a difference between the probability of finding exactly 1 defect when 1 door panel is inspected and finding exactly 2 defects when 2 doors are inspected.

orangecrush · **Reply #1 on:** Jun 24, 2018

Answer to Question 1

The binomial distribution is perfectly symmetric when p = 0.50 for any size sample. It also approaches symmetry when p is not equal to 0.50 as the sample size increases.

Answer to Question 2

First, using the Poisson distribution, the probability of exactly 1 defect when 1 door panel is inspected is 0.3614. The probability of twice that many defects (x = 2 ) when 2 door panels are examined is 0.2613. The reason that these probabilities are different, even though it might seem like they should be the same, is that when the mean is changed from 1.2 to 2.4 when going from 1 to 2 door panels, the total probability (that sums to 1.0 for the probability distribution) is spread over more possible outcomes, and that means that the probability of any one individual value occurring will be lower.