February/March 2026 Paper 52

A company sells bags of pasta. The masses of large bags of pasta are normally distributed with mean $2.40$ kg and standard deviation $0.18$ kg. In a random sample of 400 large bags, how many would you expect to have a mass less than $2.32$ kg?

The masses of small bags of pasta are normally distributed with mean $\mu$ kg and standard deviation $\sigma$ kg. $80\%$ of these bags have a mass less than $1.26$ kg and $40\%$ of these bags have a mass less than $1.08$ kg. Find the value of $\mu$ and the value of $\sigma$.

Eight small bags of pasta are chosen at random. Find the probability that more than 5 of the 8 small bags have a mass less than $1.26$ kg.