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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?

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?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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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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