An environmentalist wants to find out the fraction of oil tankers that have spills each month. Suppose a sample of 836 tankers is drawn. Of these ships, 577 did not have spills. Using the data, construct the 99% confidence interval for the population proportion of oil tankers that have spills each month.

The 99% confidence interval for the population proportion of oil tankers that have spills each month.

(0.6489 , 0.7311)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 836

Suppose a sample of 836 tankers is drawn. Of these ships, 577 did not have spills.

sample proportion

The 99% confidence interval for the population proportion is determined by

Step(ii):-

The Z- value = 2.576

On calculation , we get

(0.690 -  0.0411 , 0.690 + 0.0411)

(0.6489 , 0.7311)

Final answer:-

The 99% confidence interval for the population proportion of oil tankers that have spills each month.

(0.6489 , 0.7311)

a

step-by-step explanation:

a

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: