To determine the sample size needed to estimate the population mean with a certain level of confidence and precision, 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 level of confidence (95% confidence corresponds to a z-score of 1.96)
- σ is the standard deviation of the population
- E is the margin of error (half the width of the confidence interval, which in this case is 0.5)
Plugging in the given values, we get:
n = ((1.96 * 1.79) / 0.5)^2
n = 48.93
Rounding up to the nearest whole number, we get:
n = 49
Therefore, the answer is B. 49 students should be sampled to be within 0.5 drinks of the population mean with 95% probability.