The Normal distribution

Sample questions

Original practice questions written in the style of the exam.

1. Question 14 marks

   The lengths, $X$ cm, of leaves from a type of plant are modelled as $X \sim N(30, 5^2)$. Given $\Phi(1.4) = 0.9192$ and $\Phi(0.8) = 0.7881$, find $P(26 < X < 37)$.

   Mark scheme

   • M1 Standardise: $z = \dfrac{26 - 30}{5} = -0.8$ and $z={\displaystyle \frac{37-30}{5}}=$ (1)
2. Question 26 marks

   The masses of bags of rice filled by a machine are normally distributed with mean $\mu$ grams and standard deviation $\sigma$ grams. 10% of bags have a mass less than $495\,\text{g}$ and 5% of bags have a mass greater than $510\,\text{g}$.

   You may use $\mathrm{\Phi }($ and .