In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A shipment is acceptable if at least 440 of the 500 bearings meet the specification. Assume that each shipment contains a random sample of bearings.
a. What is the probability that a given shipment is acceptable?
b. What is the probability that more than 285 out of 300 shipments are acceptable?
c. What proportion of bearing must meet the specification in order than 99% of the shipments are acceptable?
Step 1 of 4</p>
Here given 90% of the bearings meat a thickness specification
A shipment contains 500 bearings
Let X represents no. of acceptable bearings
Here X is approximately following the normal distribution
Step 2 of 4</p>
a) Here we have to find the probability of the given shipment is acceptable
So we have to find P(X440)
Use the continuity correction find the Z value for 439.5
Now find P(Z1.49) value from the standard normal tables
Hence the probability of the given shipment is acceptable is 0.0681