Gears produced by a grinding process are categorized

Solution 14E

Step1 of 5:

We have random variable X which presents the number of gears that are scrap among the ten selected. Here 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

   = 10

x = random variable

p = probability of success

   = 5%

   = 0.05.

q = 1 - p (probability of failure)

   = 1 - 0.05

   = 0.95

Here our goal is:

a).We need to find the probability that one or more is scrap.

b).We need to find the probability that eight or more are not scrap.

c).We need to find the probability that more than two are either degraded or scrap.

d).We need to find the probability that exactly nine are either conforming or degraded.

Step2 of 5:

a).

P(One or more is scrap) = P(X1)

                                        = 1 - P(X < 1)

                                        = 1 - P(X = 0)

Consider,

       P(X) =

P(X = 0) =  

             = (1)(1)(0.5987)

             = 0.5987

Now,

P(one or more is scrap) = 1 - P(X = 0)

                        &