Question

The number of calories in a certain dessert is normally distributed with a mean of

210 and a standard deviation of 12. Find the probability that the dessert one select will

contain between 185 and 216.

Answer 1

$$P(185<X<216)=P(X<216)-P(X\le185)$$

$$=P(Z<\dfrac{216-210}{12})-P(Z\le\dfrac{185-210}{12})$$

$$\approx P(Z<0.5)-P(Z\le -2.083333)$$

$$\approx 0.69146-0.01861\approx0.6729$$