Answer to Question #279645 in Statistics and Probability for Najj

Question

What is the probability of cat weight between 5.25 kg and 6.81 kg

Answer 1

Let $X=$ the cat weight: $X\sim N(\mu, \sigma^2).$

Given $\mu=4.76kg, \sigma=1.23kg.$

$$P(5.25<X<6.81)=P(X<6.81)-P(X\leq 5.25)$$

$$=P(Z<\dfrac{6.81-4.76}{1.23})-P(Z\leq \dfrac{5.25-4.76}{1.23})$$

$$\approx P(Z<1.666667)-P(Z\leq0.398374 )$$

$$\approx 0.95221-0.65482\approx0.2974$$

The probability of cat weight between 5.25 kg and 6.81 kg is 0.2974.