Concrete blocks are produced in lots of 1000. Each block has probability of 0.90 of meeting a strength specification. The blocks are independent. a. What is the probability that, in a given lot, fewer than 890 blocks meet the specification? b. Find the 80th percentile of the number of blocks that meet the specification. c. In a group of eight lots, what is the probability that fewer than 890 blocks meet the specification in two or more of them?

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Concrete blocks are produced in lots of 1000. Each block has a probability of 0.90 of meeting a strength specification. The blocks are independent.

a. What is the probability that, in a given lot, fewer than 890 blocks meet the specification?

b. Find the 80th percentile of the number of blocks that meet the specification.

c. In a group of eight lots, what is the probability that fewer than 890 blocks meet the specification in two or more of them?
Transcribed Image Text:Concrete blocks are produced in lots of 1000. Each block has a probability of 0.90 of meeting a strength specification. The blocks are independent. a. What is the probability that, in a given lot, fewer than 890 blocks meet the specification? b. Find the 80th percentile of the number of blocks that meet the specification. c. In a group of eight lots, what is the probability that fewer than 890 blocks meet the specification in two or more of them?
Expert Solution
Step 1

Let X be the random variable that denotes number of blocks that meets specification

X~Binom(n,p)

From Given information we know that, n=1000, p=0.90

E(X)=μ=np=1000×0.9=900σ=Var(X) =np(1-p) =9.49

a) The probability that, in a given lot, fewer than 890 blocks meet the specification,

P(X<890)=P(X-9009.49<890-9009.49)=P(Z<-1.05)=(-1.05)=1-(1.05)=1-0.8531=0.1469

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