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June 2019 p61 q7
3129
The weight of adult female giraffes has a normal distribution with mean 830 kg and standard deviation 120 kg.
There are 430 adult female giraffes in a particular game reserve. Find the number of these adult female giraffes which can be expected to weigh less than 700 kg.
Solution
To find the number of giraffes weighing less than 700 kg, we first calculate the z-score for 700 kg using the formula:
\(z = \frac{X - \mu}{\sigma}\)
where \(X = 700\), \(\mu = 830\), and \(\sigma = 120\).
\(z = \frac{700 - 830}{120} = -1.083\)
Next, we find the probability that a giraffe weighs less than 700 kg, \(P(X < 700)\), which is equivalent to \(P(z < -1.083)\).
Using standard normal distribution tables or a calculator, \(P(z < -1.083) = 0.1394\).
Therefore, the expected number of giraffes weighing less than 700 kg is:
\(430 \times 0.1394 = 59.9\)
Rounding to the nearest whole number, we get 59 or 60 giraffes.