Tutorial 6 ( Mathematics T 2 )
Title : Normal Distribution
(a) A random variable X is distributed normally with mean 30 and variation 81. If
P(X ≤ a)=2P(X > a),
find the value of a, rounded to the nearest integer. Hence , find the value of
P ( 4X > 5a ).
(b) A factory produces shoes with nominal weights f 0.9 kg each. Past experience reveals
that 15% of the shoes have weights less than the nominal weight and 10% of the shoes
have weights exceeding 1.2 kg. By assuming that the weight of the shoes produced by the
factory is distributed normally, find the mean and standard deviation of the weight of a
shoe. Hence, find the probability that the total weight of 10 randomly chosen shoes will
exceed 10 kg.