Question

13. Use the appropriate normal distribution to approximate the resulting binomial distribution. Bearings is the principal supplier of ball bearings for the Sperry Gyroscope Company. It has been determined that 6% of the ball bearings shipped are rejected because they fail to meet tolerance requirements. What is the probability that a shipment of 200 ball bearings contains more than 14 rejects?

Answer 1

Answer

sample size is large enough because we have 200 ball bearings.

probability p = 6/100 = 0.06

So, probability is niether near to 0 nor near to 1

so, we can use the normal approximation.

where mean = np and

σ=Vn * p * (1-p)

we have n = 200 and p = 0.06

setting the values, we get

mean = 200*0.06 = 12

and standard deviation =

σ = V/200 * 0.06 * (1-0.06) = V 1 1.28 3.36

Now, we have to find the probability that more than 14 ball bearings rejected

So,

where

setting the given values, we get

P14) Pz> (14 - 12)/3.36)- P(z >(2/3.36))-P(z >0.5952)

using identity

wecan write it as

(using z distribution table)

P(z > 0.5952) = 1-P(z < 0.5952) 1-0.7257 = 0.2743

So, the required probability is 0.2743