Question

Step 1

Area under the normal curve is the sum of all probabilities of variable X. Since probability ranges from 0 to 1, the total area under the cuve is equal to 1. We can calculate the probability of finding a score/number less than X ie P(x<X) by calculating Z score and the finding corresponding probability of that Z score using Z table.

But if we need to find probability of a score greater than X ie P(x>X) then we first calculated P(x<X) and subtract that from 1.

Step 2

Part a)

Z score computation:

Step 3

Probability corresponding to Z score of 0.5 can be read from z table as shown below.

P(X<60)=P(Z<0.5) = ...

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