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%.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional