2.4.12 Calculate probabilities from a Normal distribution (A-level only)

The weights of newborn puppies in a specific breed, $W$ grams, are normally distributed with $\sim \text{N}(450, 40^2)$ .

Find the probability that a randomly selected puppy weighs less than 510 g.

[2]

Find the upper quartile, $Q_3$ , of $W$ .

[2]

Write down the lower quartile, $Q_1$ , of $W$ .

[1]

An outlier is defined as any value of $W$ such that $W < h$ or $W > k$ , where

Q_1 - 1.5 \times (Q_3 - Q_1) \quad \text{and} \quad k = Q_3 + 1.5 \times (Q_3 - Q_1)

Find the value of $h$ and the value of $k$ .

[2]

Find the probability that a randomly selected puppy’s weight is an outlier.

[3]

2.4.12 Calculate probabilities from a Normal distribution (A-level only) Questions