Answer to Question #334929 in Statistics and Probability for Isy

Question

The weights of a large number of miniature poodle are approximately normally distributed with a mean of 8 kilograms and a standard deviation of 0.9 kilograms. If measurements are recorded to the nearest tenth of a kilogram, find the fraction of these poodle

Answer 1

Let $X=$the weight of a miniature poodle: $\sim N(\mu, \sigma^2).$  

a.

$$P(X>9.5)=1-P(Z\le\dfrac{9.5-8}{0.9})$$

$$\approx0.0478$$

b.

$$P(X\le8.6)=P(Z\le\dfrac{8.6-8}{0.9})\approx0.7475$$

c.

$$P(7.3\le X\le9.1)=P(Z\le\dfrac{9.1-8}{0.9})$$

$$-P(Z\le\dfrac{7.3-8}{0.9})\approx0.6708$$