Answer to Question #139869 in Statistics and Probability for Stellar Jennie

Question

The population mean weight of a candy is 10 grams with a standard deviation of 2 grams. A sample of 100 candies is taken. What is the probability that the sample mean is between 9.4 and 10.4 grams?

Answer 1

We need to compute $P(9.4 \le \bar X \le 10.4)$. The corresponding z-values needed to be computed are:

$Z_1 = \frac{\bar X_1 - \mu}{\sigma/\sqrt n}= \frac{ 9.4-10}{ 2/\sqrt{100}} = -3$

$Z_2 = \frac{\bar X_2- \mu}{\sigma/\sqrt n}= \frac{ 10.4-10}{ 2/\sqrt{100}} = 2$

$P(9.4≤ \bar X ≤10.4)=P(-3≤Z≤2)=P(Z≤2)-P(Z≤-3)=0.97725-0.00135=0.9759$