2.(A) A nation-wide survey carried out on behalf of the central government revea

Question

2.(A) A nation-wide survey carried out on behalf of the central government revealed that 25% of the households do not possess a car.

(a) What is the probability that in a random sample of 10 households more than three do not possess a car?

(b) What is the probability that ip a random sample of 1,800 households more than 420 do not possess a car?

(B) In the month of March 2016 the owner of Sally's Hardware received a lot of twelve gas lawnmowers from the manufacturer. Unknown to the owner four lawnmowers of the lot were substandard.

(a) The first week of April 2016 Sally's Hardware sold six lawnmowers. What is the probability that at least three were not substandard?

(b) Let X denote the number of substandard lawnmowers in a random sample of six lawnmowers. Write down the probability distribution of X.

Explanation / Answer

Ans:

2)Binomial distribution

p=0.25

a)n=10

P(k>3)=1-P(k<=3)=1-BINOMDIST(3,10,0.25,TRUE)=1-0.7759=0.2241

b)As nis too large here,we can do the Normal approximation

Mean=np=1800*0.25=450

std dev=sqrt(450*(1-0.25))=18.37

P(x>420)

z=(420-450)/18.37=-1.633

P(z>-1.633)=1-P(z<=-1.633)=1-0.0512=0.9488

using binomial distribution:

P(k>420)=1-P(k<=420)=BINOMDIST(420,1800,0.25,TRUE)=1-0.0533=0.9467

3)p=4/12=0.33

n=6

a)P(k>=3)=1-P(k<=2)=1-BINOMDIST(2,6,0.33,TRUE)=1-0.6870=0.313

b)Binomial distribution

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