Answer to Question #181909 in Statistics and Probability for Rica mallari

Question

The average number of milligrams (mg) of cholesterol in a cup of certain brand of ice cream is 660 mg, and the standard deviation is 35 mg. assume the variable is normally distrubuted.

If a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger than 670 mg

Answer 1

Let $X=$  the mean of the sample: $X\sim N(\mu, \sigma^2/n).$

Given $\mu=660\ mg, \sigma=35\ mg, n=10$

$$P(X>670)=1-P(X\leq670)$$

$$=1-P(Z\leq\dfrac{670-660}{35/\sqrt{10}})$$

$$\approx1-P(Z\leq0.9035)\approx0.1831$$

The probability that the mean of the sample will be larger than 670 mg is 0.1831.