An industrial plant dumps its waste into a nearby river, but claims that it is not impacting the native fish that live in the river. you’ve measure the calcium concentration from a random sample of 24 locations in the river and calculated a mean of 98.4 mg/l, with a standard deviation of 5.1 mg/l. the fish are able to tolerate calcium concentrations up to 95 mg/l. assuming a normal distribution, calculate a 95% confidence interval for the mean calcium concentration in the river.

The 95% confidence interval  for the mean calcium concentration in the river is (96.2482mg/L, 100.5518mg/L).

Step-by-step explanation:

Our sample size is 24.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

.

Then, we need to subtract one by the confidence level and divide by 2. So:

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 23 and 0.025 in the two-sided t-distribution table, we have

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

Now, we multiply T and s

Then

The lower end of the confidence interval is the mean subtracted by M. So:

The upper end of the confidence interval is the mean added to M. So:

The 95% confidence interval  for the mean calcium concentration in the river is (96.2482mg/L, 100.5518mg/L).

a² + b²= c²

24² + 7² = c²

c= 25