4.1.1 Probability (A-level only)

The masses of a specific breed of adult dog are normally distributed with a mean of $kg24\text{ kg}$ and a standard deviation of $kg5\text{ kg}$ .

Find the probability that a randomly selected dog from this breed has a mass greater than $kg31.5\text{ kg}$ .

[3]

Any dog of this breed with a mass greater than $kg31.5\text{ kg}$ is classified as "heavy".

A dog of this breed is chosen at random. Given that it is classified as heavy,

find the probability that it has a mass greater than $kg36\text{ kg}$ .

[4]

Among the heavy dogs, exactly $25%25\%$ have a mass greater than $kgm\text{ kg}$ .

Find the value of $m$ .

[4]

4.1.1 Probability (A-level only) Questions