A process produces batches of a chemical whose impurity concentrations follow a normal distribution with a variance of 1.75. A random sample of 20 of these batches is chosen. Find the probability that the sample variance exceeds 3.10.

Probability that the sample variance exceeds 3.10 is less than 0.05%.

Step-by-step explanation:

We are given that a process produces batches of a chemical whose impurity concentrations follow a normal distribution with a variance of 1.75.

Also, a random sample of 20 of these batches is chosen.

The probability distribution that we will used here is of Chi-square distribution, i.e.;

                    ~

where, = sample variance

            = population variance = 1.75

            n = sample of batches = 20

So, probability that the sample variance exceeds 3.10 is given by = P( > 3.10)

        P( > 3.10) = P( > )

                           = P( > 59.62) = P( > 59.62) = Less than 0.05%

From chi-square table we can observe that Probability that is greater than is less than 0.05%.                      

So, the probability that the sample variance exceeds 3.10 is less than 0.05%.