Question

To estimate the proportion of brand-name lightbulbs that are defective, a simple random sample of 400 brand-name lightbulbs is taken and 44 are found to be defective. Let X represent the number of brand-name lightbulbs that are defective in a sample of 400, and let PXrepresent the proportion of all brand-name lightbulbs that are defective. It is reasonable to assume that X is a binomial random variable.
Requried:
One condition for obtaining an interval estimate for Px is that the distribution of Px is approximately normal. Is it reasonable to assume that the condition is met?

Answer 1

Answer:

X is a binomial random variable

Then the condition is met

Step-by-step explanation:

Sample size   n₁  = 400

X represents the number of brand-name lightbulbs)

P(X) = 44/400

P(X) = 0,11

X  is a binomial random variable it only could be either no defective or defective ( only two conditions or values).

To make use of the condition of approximation of binomial distribution to a normal distribution it is required that the products:

p*n  =  0,11*400  =  44      and    q  =  1  - 0,11   q =  0,89

q*n  =  0,89 * 400  =  356

both  p*n  q*n  are greater than 5.

Then the condition is met