Answer to Question #178383 in Statistics and Probability for Anyama Priscilla

Question #178383

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 distribution if a random

Sample of 200 cars were selected at Tema Port


1
Expert's answer
2021-04-15T07:52:54-0400

We have that:

p = 10% = 0.1

n = 5

This follows the binomial distribution.

The binomial probability is calculated by the formula:


"P(X=m)=C(n,m)\\cdot p^m \\cdot(1-p)^{n-m}"

i) m = 3

"P(X=3) = C(5,3)\\cdot 0.1^3 \\cdot 0.9^{5-3}=\\frac{5!}{3!2!}\\cdot0.1^3\\cdot0.9^2=0.0081"

ii) m = 2

"P(X=2) = C(5,2)\\cdot 0.1^2 \\cdot 0.9^3=0.0729"

iii) m = 0

"P(X=0) = C(5,9)\\cdot 0.1^0 \\cdot 0.9^5=0.59049"

iv) n = 200

The mean is calculated by the formula:

"\\mu = np=200\\cdot 0.1=20"

The standard deviation is calculated by the formula:

"\\sigma=\\sqrt{np(1-p)}=\\sqrt{200\\cdot0.1\\cdot0.9}=4.24"


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