Answer to Question #214648 in Macroeconomics for reenam

Question

Suppose a survey by the Department of Roads in 2019 revealed that 60% of the vehicles travelling on Suva-Nadi Highway, where speed limits are posted at 80 kilometres per hour are found to be exceeding the limit. Suppose you randomly record the speed of 10 vehicles travelling on the highway as part of your internship. The sample size of the entire survey is not disclosed to you. Compute the following probabilities. Showing all working. a) P (X = 2). [3 marks] b) P (X = 5). [3 marks] c) P (X = 10)

Answer 1

It is given that

$60$$\%$% is the percentage of vehicles traveling on highway = $0.60$

The number of cars sampled= $10$

The speed limit = $80km/h$

Assume that X is the number of vehicles that exceeds the limit in the 10 sampled vehicle.

$X = Binom( n=10, P= 0.60)$

$P(X=n) = \begin{pmatrix} 10\\ n \end{pmatrix}$$\times (0.60)^n \times (1-0.6)^{10-n}$

a)

$P(X=2)$ = $= \begin{pmatrix} 10\\ 2 \end{pmatrix}$$× (0.60)^2× (1-0.60)^{10-2} = 0.0106$

 P(x=2)= 0.0106

b)

= $P(X= 5)= \begin{pmatrix} 10 \\ 5 \end{pmatrix} ×(0.60)^5 × (1-0.60)^{10-5}= 0.2007$

P(x=5)= 0.2007

c)

$P(X = 10)= \begin{pmatrix} 10\\ 10 \end{pmatrix}× (0.60)^10 ×(1-0.60)^{10-10} = 0.0061$