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Nov 2011 p63 q6
3325
Human blood groups are identified by two parts. The first part is A, B, AB or O and the second part (the Rhesus part) is + or −. In the UK, 35% of the population are group A+, 8% are B+, 3% are AB+, 37% are O+, 7% are A−, 2% are B−, 1% are AB− and 7% are O−.
A random sample of 150 people in the UK is taken. Find the probability that more than 60 people are group A+.
Solution
Let the random variable representing the number of people with blood group A+ be denoted by \(X\). Given that 35% of the population are group A+, we have \(p = 0.35\).
The sample size is \(n = 150\). The mean \(\mu\) and variance \(\sigma^2\) of \(X\) are given by:
\(\mu = n \times p = 150 \times 0.35 = 52.5\)
\(\sigma^2 = n \times p \times (1-p) = 150 \times 0.35 \times 0.65 = 34.125\)
We use the normal approximation to the binomial distribution. Applying continuity correction, we find: