Question

Suppose the mean number of days to germination of a variety of seeds is 22, with a standard deviation of 2.3 days. Find the probability that the mean germination time of a sample of 160 seeds will be within 0.5 days of the population mean.

Answer 1

$$P(-\dfrac{0.5}{2.3/\sqrt{160}}<Z<\dfrac{0.5}{2.3/\sqrt{160}})$$

$$\approx P(Z<2.7498)-P(Z\le-2.7498)$$

$$\approx0.99702-0.00298=0.9940$$