Question

Apple® knows that 8% of its Macbook Pro computers will have a defective part requiring at least $200 in service within the first 6 months. What is the probability that a batch of 10 Macbooks will contain: (a) no more than 2 Macbooks with defective parts and (b) at least 2 Macbooks with defective parts? What is the expected value and standard deviation of defective Macbooks?

(show in excel with functions)

Answer 1

Let X be a number Mackbooks with defective parts among 10 Mackbooks

Here, X ~ Binomial (n = 10, p = 0.08)

Using Excel we function "BINOMDIST" we find the following probabilities,

a) P(X ≤ 2) = BINOMDIST(2, 10, 0.08, 1) = 0.959925

Therefore, required probability is 0.959925

b) P(X ≥ 2)

= 1 - P(X ≤ 1)

= 1 - BINOMDIST(1, 10, 0.08, 1)

= 0.187882

Therefore, required probability is 0.187882

Expected value = mean = np = 10 * 0.08 = 0.8

=> Expected value = 0.8

standard deviation =

=> Standard deviation = 0.857904