Question

Concrete blocks are produced in lots of 2000. Each block has probability 0.85 of meeting a strength specification. The blocks are independent.

NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

1-What is the probability that, in a given lot, fewer than 1690 blocks meet the specification?

2-Find the 70th percentile of the number of blocks that meet the specification.

3-In a group of six lots, what is the probability that fewer than 1690 blocks meet the specification in three or more of them?

Answer 1

Answer:

Given that:

Concrete blocks are produced in lots of 2000. Each block has probability 0.85 of meeting a strength specification. The blocks are independent.

Using Binomial distribution we have average number of blocks that meet the specification is

   and the standard deviation is

Now using the normal approximation to binomial distribution we define the standard random variable Z as

where X denotes the number of blocks that meet the specification

1) What is the probability that, in a given lot, fewer than 1690 blocks meet the specification?

Using normal table we have

2) Find the 70th percentile of the number of blocks that meet the specification.

Since from the normal table we have

So

So approximately 1708 number of blocks that meet the specification

3) In a group of six lots, what is the probability that fewer than 1690 blocks meet the specification in three or more of them?

Using 1) we have 1 lot has probability 0.2655  that fewer than 1690 blocks meet the specification So using binomial distribution we have out of six lots 3 or more lots will have fewer than 1690 blocks that meet the specification is given by