Refer to Example 4.14. Estimate the probability that

Solution 25E

Step1 of 3:

Let us consider a random variable X it presents the number of tires out of four that have no flaw.

Also from Example 4.14 we have sample proportion and standard deviation  Let “q” be the probability that exactly one of four tires has a flaw.

Then X follows binomial distribution with parameters “n and p” that is X B(n, p),

The probability mass function of binomial distribution is given by

, x = 0,1,2,...,n.

Where,

n = sample size

   = 4

x = random variable

p = probability of success

q = 1 - p (probability of failure)

We need to Estimate the probability that exactly one of the four tires has a flaw, and also we need to find the uncertainty in the estimate.

Step2 of 3:

Consider,

Let q = P(X = 3)

Now,