SOLUTION: Use the normal approximation to the binomial distribution to find the probability that at most 40 of 225 loan applications received by a bank will be refused, if the probability is

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Question 1153909: Use the normal approximation to the binomial distribution to find the probability that at most 40 of 225 loan applications received by a bank will be refused, if the probability is 0.12 that such application will be refused. (6marks)

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


The desired approximation is the probability that x lies below 40.5,
using those values of the mean and standard deviation. 

P%28x%3C40.5%29

Get the z-scores for that value and we find that it equals:

P%28z%3C2.77%29

Look up z=2.7 and go across to the column for 0.07 

There are two kinds of normal tables in use today.

If you read 0.9972, that's the answer

If you read 0.4972, add 0.5000 and get 0.9972.

The TI-83 or TI-84 calculator gives a more accurate answer than can
be gotten through tables.  But they both round to 1.00  So "almost certain"
is about as close as you're going to get.

Edwin