A certain type of aluminum screen 2 feet in width has, on the average, three flaws in a l00-foot roll.

(a) What is the probability that the first 40 feet in a roll contain no flaws?

(b) What assumption did you make to solve part (a)?

Solution 6E

Step1 of 3:

We have aluminium screen it has width 2 feet and on the average, three flaws in a l00-foot roll.

That is x = 3 and n = 100.

We need to find,

(a) What is the probability that the first 40 feet in a roll contain no flaws?

(b) What assumption did you make to solve part (a)?

Step2 of 3:

Let “X” be random variable which follows poisson distribution with parameters .

That is X P()

The probability mass function of binomial distribution is given below

P(X) = , x =0,1,2,3,...,n.

Where,

X = random variable

n = sample size

p = probability of success(or proportion).

e = a constant it is approximately 2.7182.

Here we have mean

= 0.03

Hence, = 0.03.

Let Y = number of feet before 1st flaw

Pdf is given by

f(Y) =

a).

The...