Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

The length of each phone call Moses makes has a normal distribution with mean 6.5 minutes and standard deviation 1.76 minutes.
(i)[3]

90% of Moses's phone calls last more than $t$ minutes. Find the value of $t$.

(ii)[5]

Find the probability that, in a random sample of 9 phone calls made by Moses, more than 7 have a duration that is within 1 standard deviation of the mean.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: The rounded value is $z = -1.28$.

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