Question

Student Number For the following written questions, write out ALL of your work to get full marks (Question 10- 4 marks) A key machine makes keys with some aaon forjation error. We expect there mEm I to be aero error but the amount is normally distributed with standard the error is no more than 1 mm the key will work ne 0.7 deviation a)What is the probability that a key made will work (the error is no more than 1 mm)? b) If you have 5 keys made independently, what is the probability that exactly 3 keys will wor

Answer 1

a) P(a key will work)

= P(-1 < X < 1)

= P((-1 - $\mu$)/$\sigma$ < (X - $\mu$)/$\sigma$ < (1 - $\mu$)/$\sigma$)

= P((-1 - 0)/0.7 < Z < (1 - 0)/0.7)

= P(-1.43 < Z < 1.43)

= P(Z < 1.43) - P(Z < -1.43)

= 0.9236 - 0.0764

= 0.8472

b) n = 5

p = 0.8472

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

P(X = 3) = 5C3 * (0.8472)^3 * (1 - 0.8472)^2

               = 0.1420