In a certain type of automobile engine, the cylinder head is fastened to the block by 10 bolts, each of which should be torqued to 60 N • m. Assume that the torques of the bolts are independent.

a. If each bolt is torqued correctly with probability 0.99, what is the probability that all the bolts on a cylinder head are torqued correctly?

b. The goal is for 95% of the engines to have all their bolts torqued correctly. What must be the probability that a bolt is torqued correctly in order to reach this goal?

Step 1 of 3:

It is given that 10 bolts are used to fasten a cylinder head to a block.

It is assumed that the torques of the bolt are independent.

Using these,we have to find the required probabilities.

Step 2 of 3:

(a)

It is given that each bolt is torqued correctly with 0.99 probability,

We have to find the probability that all the bolts on the cylinder are torqued correctly.

That is we have find P(all bolts are torqued correctly).

We know that all are torques of the bolt are assumed to be independent.

So,

P(all bolts are torqued correctly)=P(1st bolt torqued correctly)P(2nd bolt torqued correctly)P(3rd bolt torqued correctly)P(4th bolt torqued correctly)P(5th bolt torqued correctly)P(6th bolt torqued correctly)P(7th bolt torqued correctly)P(8th bolt torqued correctly)P(9th bolt torqued correctly)P( 10th bolt torqued correctly)

=0.99*0.99*0.99*0.99*0.99*0.99*.0.99*0.99*0.99*0.99

=

=0.9043.

Thus,the probability that all the bolts are torqued correctly is 0.9043.