Answer to Question #146594 in Statistics and Probability for hafiey

Question

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

Answer 1

Mean = 22

Sd = 2.3

Standard deviation of sampling distribution $= \frac{Sd}{\sqrt{n}}$

Standard deviation of sampling distribution $= \frac{2.3}{\sqrt{160}} = 0.1818$

Probability $= P(\frac{-0.5 }{ 0.1818} < Z < \frac{0.5}{0.1818})$

Probability = P(-2.75 < Z < 2.75)

Probability = P(Z < 2.75) – P(Z < -2.75) = 0.997 – 0.003 = 0.9940

Answer: 0.994