Answer to Question #178109 in Statistics and Probability for Tahiru Rabiu

Question

A research was conducted in 2017 at the Tema Port to find the ages of cars imported into 

the country. According to the research, 10% of the cars imported were less than one-year￾old. Assuming this result holds true for the current period for all cars imported into the 

country.

Find the probability that in a random sample of 5 cars at the Tema Port

(i) exactly 3 are less than one-year-old.

(ii) exactly 2 are less than one-year-old.

(iii) none is less than one-year-old 

(iv) Find the mean and standard deviation of the distrib

Answer 1

This is a binomial distribution with p=0.1, n=5.

(i) $P(X=3)=C_5^30.1^3(1-0.1)^2=0.0081.$

(ii) $P(X=2)=C_5^20.1^2(1-0.1)^3=0.0729.$

(iii) $P(X=0)=(1-0.1)^5=0.5905.$

(iv) $\mu=np=5*0.1=0.5.$

$\sigma=\sqrt{np(1-p)}=\sqrt{0.45}=0.6708.$