Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The times that students take to get out of bed in the morning can be represented by a normal distribution with mean 26.4 minutes and standard deviation 3.7 minutes.
(i)[3]
For a random sample of 350 students, determine how many would be expected to take more than 20 minutes to get up in the morning.
(ii)[4]
‘Very slow’ students are those whose time to get up is more than $1.645$ standard deviations above the mean. Find the probability that fewer than 3 students in a random sample of 8 students are ‘very slow’.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Standardise correctly, for example $P(X>20)=P(Z>-\frac{6.4}{3.7})$” …