Answer to Question #300316 in Statistics and Probability for geru

Question

A coke float machine dispenses into 18-ounce cups. Test show that the actual amount of ice cream dispensed is normally distributed with a mean of 12.75 oz. and a standard deviation of 0.27 oz.

a. what percent of cups will receive 12.25 oz of ice cream?

b. wha percent of cups will receive less than 12.15 oz. of ice cream?

Answer 1

Let $X=$ the amount of  of ice cream in a cup: $N(\mu, \sigma^2).$

Given $\mu=12.75, \sigma=0.27.$

a.

$$P(X=12.25)=0$$

$0\%$

b.

$$P(X<12.15)=P(Z<\dfrac{12.15-12.75}{0.27})$$

$$\approx P(Z<-2.2222)\approx0.013341$$

$1.33\%$