Suppose that 80 of the cars on the road have improperly infl

Suppose that 80% of the cars on the road have improperly inflated tires. Find the probability that a random sample of 10 cars will show:

(a) Exactly 7 with improperly inflated tires.

(b) Between 5 and 7 (inclusive) with improperly inflated tires.

(c) At least 7 with improperly inflated tires.

Solution

let X be the random variable which represents number of improperly inflated tires

x follows binomial distribution

a)

P(X=7) = 10C7 * 0.8^7 * 0.2^3 = 0.2013

b)

P(5<= X<= 7) = P(X=5) + P(X=6) + P(X=7)

= 10C5 * 0.8^5 * 0.2^5 + 10C6 * 0.8^6 * 0.2^4 + 10C7 * 0.8^7 * 0.2^3

= 0.3158

c)

P(X>-7) = P(X=7) + P(X=8) + P(X=9) + P(X=10)

= 10C10 * 0.8^10 * 0.2^0 + 10C9 * 0.8^9 * 0.2^1 + 10C8 * 0.8^8 * 0.2^2 + 10C7 * 0.8^7 * 0.2^3

= 0.8791