Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The lengths, in cm, of trout in a fish farm follow a normal distribution. 96% of the lengths are below 34.1 cm, and 70% of the lengths are above 26.7 cm.
(i)[5]
Determine the mean and the standard deviation of the trout lengths.
(ii)[3]
In a different fish farm, the lengths of salmon, X cm, are normally distributed with mean 32.9 cm and standard deviation 2.4 cm. Find the probability that a salmon chosen at random is 34 cm long, correct to the nearest centimetre.
(iii)[4]
Find the value of t such that \mathrm{P}(31.8 < X < t) = 0.5.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies \frac{34.1-\mu}{\sigma}=1.751 or equivalent.” …