Question

A bottling process is inspected 100 percent of the time because of the low yield rate of 98%. If a batch of 80 bottles are inspected, what is the probability less than three bottles are bad?

Answer 1

Answer:784 i think

Explanation:

98 x 8 = 784. My teacher told me that when multiplying %'s you do the precent # x the #

Answer 2

The probability is
`P(X <  3) =  0.7843`

Explanation:

From the question we are told that

The low yield rate is
`q = 0.98`

The sample size n = 80

Hence the probability that the bottle is bad

`p = 1- q`

=>
`p = 1 - 0.98`

=>
`p =0.02`

Generally the distribution of yield follows a binomial distribution

i.e

`X  \~ \ \ \  B(n , p)`

and the probability distribution function for binomial distribution is

`P(X = x) =  ^(n)C_x *  p^x *  (1- p)^(n-x)`

Here C stands for combination hence we are going to be making use of the combination function in our calculators

Generally the probability less than three bottles are bad is mathematically represented as

`P(X <  3) = P(X = 0 ) + P(X = 1 )+ P(X = 2)`

=>
`P(X <  3) = ^(80)C_0 *  0.02^0 *  (1- 0.02)^(80-0) +^(80)C_1 *  0.02^1 *  (1- 0.02)^(80-1)+ ^(80)C_2 *  0.02^2 *  (1- 0.02)^(80-2)`

=>
`P(X <  3) = 1 *  1 * 0.1986 + 80 *  0.02 *  0.2027 + 3160 *  0.0004 * 0,2068`

=>
`P(X <  3) =  0.7843`