A manufacturer produces thermostats,10% of which are defective.From a production run,a sample of four thermostats is randomly selected.Determine the probability that at least three of the selected thermostats are defective.You may assume that the four trials are independent and that the number of defective items in the sample has a binomial distribution.
A) 0.0035
B) 0.0036
C) 0.0037
D) 0.0038
E) 0.0039

Question

Quizplus · Accepted Answer

To find the probability that at least three of the selected thermostats are defective, we need to calculate the probability of getting 3 defective thermostats and the probability of getting 4 defective thermostats and then add them together.

Using the binomial distribution formula, we can calculate the probability of getting exactly 3 defective thermostats:

P(X=3) = (4 choose 3) * (0.1)^3 * (0.9)^1 = 4 * 0.001 * 0.9 = 0.0036

Similarly, we can calculate the probability of getting 4 defective thermostats:

P(X=4) = (4 choose 4) * (0.1)^4 * (0.9)^0 = 0.0001

Now we add these probabilities together:

P(at least 3 defective) = P(X=3) + P(X=4) = 0.0036 + 0.0001 = 0.0037

Therefore, the best choice is C) 0.0037.

A Manufacturer Produces Thermostats,10% of Which Are Defective