S1 June 2010 Q7

EdexcelOld spec12 marksNormal Distribution

7. The distances travelled to work, \(D\) km, by the employees at a large company are normally distributed with \(D \sim \mathrm{N}(30, 8^2)\).

(a) Find the probability that a randomly selected employee has a journey to work of more than 20 km. (3)
(b) Find the upper quartile, \(Q_3\), of \(D\). (3)
(c) Write down the lower quartile, \(Q_1\), of \(D\). (1)

An outlier is defined as any value of \(D\) such that \(D \lt h\) or \(D \gt k\) where

\[h = Q_1 - 1.5 \times (Q_3 - Q_1) \quad \text{and} \quad k = Q_3 + 1.5 \times (Q_3 - Q_1)\]
(d) Find the value of \(h\) and the value of \(k\). (2)

An employee is selected at random.

(e) Find the probability that the distance travelled to work by this employee is an outlier. (3)
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