Find the probability of 1 tire with low air pressure P (1)

[Crowbarr]

1) Let X represent the number of tires with low air pressure on a randomly chosen car. The probability of distribution of X is as follows:
X 0 1 2 3 4
P(X) 0.1 0.2 0.4 0.2 0,1

a) Find the probability of 1 tire with low air pressure P (1) =

b) Find the probability of more than 2 tires having low air pressure P (more than 2) =

c) P (all 4 tires) =

d) Compute the expected number of tires with low air pressure.

e) Compute the standard deviation for the number of tires with low air pressure.

 

[jvicens]

a) P(1) = 0.2

b) P(more than 2) = P(3) + P(4) = 0.2 + 0.1 = 0.3

c) P(all 4 tires) = 0.1

d) The expected number of tires with low air pressure can be calculated by multiplying each possible number of tires with its corresponding probability and adding them together.
Expected number = (0*0.1) + (1*0.2) + (2*0.4) + (3*0.2) + (4*0.1) = 1.6 tires

e) The standard deviation for the number of tires with low air pressure can be calculated using the formula:
Standard deviation = √(∑(x-μ)^2 * P(x))
where μ is the expected value and P(x) is the probability of x tires with low air pressure.
In this case, it would be:
Standard deviation = √(0.1*(0-1.6)^2 + 0.2*(1-1.6)^2 + 0.4*(2-1.6)^2 + 0.2*(3-1.6)^2 + 0.1*(4-1.6)^2)
= √(0.16 + 0.04 + 0.16 + 0.04 + 0.16)
= √0.56
= 0.75 tires