May/June 2026 Paper 51

The heights of adult Indian elephants are normally distributed with mean $2.74$ m and standard deviation $0.25$ m. A random sample of 250 of these elephants is chosen. How many of these 250 elephants would you expect to have a height between $2.40$ m and $3.10$ m?

The heights of adult African elephants are normally distributed with mean $\mu$ m and standard deviation $0.28$ m. It is known that $62\%$ of adult African elephants have a height greater than $3.15$ m. Find the value of $\mu$.

A random sample of 90 adult African elephants is chosen. Use an approximation to find the probability that more than 50 of these 90 elephants have a height greater than $3.15$ m.