Question

From past experience, it is known that the weights of salmon grown at a commercial hatchery are normal with a mean that varies from season to season but with a standard deviation that remains fixed at 0.3 pounds. If we want to be 95 percent certain that our estimate of the present season’s mean weight of a salmon is correct to within ±0.1 pound, how large a sample size is needed?

a) 44
b) 64
c) 84
d) 104

Answer 1

To estimate the present season's mean weight of a salmon within ±0.1 pound with 95% confidence, a sample size of 46 is needed.

Step-by-step explanation:

To calculate the sample size needed to estimate the present season's mean weight of a salmon, we can use the formula:

n = (Z * σ / E) ^ 2

where n is the sample size, Z is the z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence), σ is the standard deviation of the population (0.3 pounds), and E is the desired margin of error (0.1 pound).

Plugging in these values:

n = (1.96 * 0.3 / 0.1) ^ 2 = 45.6

Rounding up to the nearest whole number, we need a sample size of 46.