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2.4.4 Mean and variance of the binomial (A-level only)

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Question 42

The time, in minutes, spent by a technician to calibrate a sensor is modelled by the random variable TTT with probability density function

f(t)={1225(30t−3t2)0≤t≤50otherwise f(t) = \begin{cases} \frac{1}{225}(30t - 3t^2) & 0 \le t \le 5 \\ 0 & \text{otherwise} \end{cases} f(t)={2251​(30t−3t2)0​0≤t≤5otherwise​
a.

Use algebraic integration to find, in minutes and seconds, the mean calibration time.

[3]
b.

Show that P(1<T<4)=1825P(1 < T < 4) = \frac{18}{25}P(1<T<4)=2518​.

[4]
c.

A quality control manager randomly selects 100 calibration sessions.

Use a suitable approximation to find the probability that at least 75 of these sessions take between 1 and 4 minutes.

[5]

2.4.4 Mean and variance of the binomial (A-level only) Questions

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