Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
At Breven college, the heights of the female students follow a normal distribution:
• $90\%$ of the female students are shorter than $182.7$ cm.
• $40\%$ of the female students are shorter than $162.5$ cm.
(a)[5]
Calculate the mean and the standard deviation for the heights of the female students at Breven college.
(b)[3]
Ten female students are selected at random from the Breven college group. Find the probability that fewer than $8$ of these $10$ students are taller than $162.5\text{ cm}$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Gives the correct critical $z$-values $\pm1.282$ and $\pm0.253$” …