Question

3. The technology known as 3D printing has come a long way in just a few years, but the machines still tend to be prone to errors that totally ruin what they’re trying to make. A small company has a machine that has a 93% success rate in making a perfect part. Today, they have scheduled to make 25 parts.

a. Does the number of perfect parts follow a binomial model? Check the conditions on page 128. Answer in a complete sentence for each one.

b. Assuming the binomial model does apply, what is the probability that the machine produces 23 or more perfect parts?

c. What is the probability that the machine produces fewer than 20 perfect parts?

Answer 1

(a)

The number of perfect parts follow binomial model, as it satisfies all the conditions:

(i) The experiment consists of n identical trials. Here n = 25 fixed.

(ii) Each trial results in one of the two outcomes: called success and failure: here: perfect and imperfect

(iii) The probability of success p remains the same. here: p = 0.93 fixed

(iv) The n trials are independent. here all parts are independent

(b)

n = 25

p = 0.93

q = 1 - p = 0.07

P(X23) = P(X=23) + P(X=24) + P(X=25)

So,

P(X23)=0.7466

So,

Answer is

0.7466

(c)

P(X<20) = 1 - [P(X=20) + P(X=21) + P(X=22)+P(X+23)+P(X=24)+P(X=25)]

So,

P(X<20) = 1 - 0.9935

           = 0.0065

So,

Answer is:

0.0065