The Normal Distribution


Exercises for students
Solve the following problems on paper and check your working using the above applet:

Given X ~ N(0, 1). Calculate P(X < 0), P(X < 1), P(X > 1), P(1 < X < 2),
P(X < 1 or X > 2), P(X < -1), P(X > -1), P(-1 < X < 2), P(-2 < X < -1).

Given X ~ N(2, 4). Calculate P(X < 4), P(X > 4), P(X < 1), P(X > 1),
P(1 < X < 4), P(X < 1 or X > 4), P(0 < X < 4), P(0 < X < 1).


The weight of watermelons may be taken to have a normal distribution with mean 6 kg and standard deviation 2 kg.
One watermelon is chosen at random. Find the probability that
(a) it weighs more than 5 kg.
(b) its weight lies between 4 kg and 7 kg.

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