Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

The lengths of time that people spend at a particular dentist are mutually independent and follow a normal distribution with mean $8.2$ minutes. $79\%$ of the people who visit this dentist have appointments lasting under $10$ minutes.
(a)[3]

Calculate the standard deviation of the times spent by people visiting this dentist.

(b)[3]

Find the probability that the time spent visiting this dentist by a randomly chosen person deviates from the mean by more than $1$ minute.

(c)[3]

Find the probability that, out of $6$ randomly selected people, more than $2$ have visits lasting longer than $10$ minutes.

(d)[5]

Find the probability that, of $35$ randomly chosen people, fewer than $16$ have visits lasting less than $8.2$ minutes.

Worked solution & mark scheme

This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: $z=0.807$

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