Answer to Question #194550 in Macroeconomics for fahmida

Question

4. Suppose that in Dhaka, twenty-three percent of automobiles are not covered by insurance. On  a particular weekend, 35 automobiles are involved in traffic accidents. a. What is the expected number of these automobiles that are not covered by insurance? b. What are the variance and standard deviation?

1. Suppose that in Dhaka, 30% of workers take public transportation daily (USA Today,  December 21, 2005). a. In a sample of 10 workers, what is the probability that exactly three workers take public  transportation daily? b. In a sample of 10 workers, what is the probability that at least three workers take public transportation daily?

Answer 1

4.

a.

The sample of automobiles is ,n=35.

The probability of automobiles not covered by insurance is, 0.023.

The expected number of these automobiles that are not covered by insurance is,

$E(x)=np\\=35\times 0.23\\=8.05\\\approx 8$

b

The variance is calculated as,

$V(x)=np(1-p)\\=35\times0.023(1-0.023)\\6.2$

The standard deviation is,

$SD=\sqrt V\\=\sqrt {6.2}\\=2.49$

1.

p=30%=0.3

n=10

Formula binomial probability:

$f(k)=({n \atop k}) .p^k.(1-p)^{n-k}$

a.

$f(3)=({10 \atop3}).0.30^3.(1-0.30)^{10-3}\approx 0.2668$

b.

Add the corresponding probabilities:

$P(X\ge3)\\=f(3)+f(4)+f(5)+f(6)+f(7)+f(8)+f(9)+f(10)\\\approx0.6172$