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Ans. P 0.97. 12. Suppose an event A has probability suppose an event A has probability 0.4. How many trials must be performed
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Answer #1

Solution:

Given:

p = probability of an event A = 0.4

c = confidence level = 0.9 that is: 90%

E = margin of Error = 0.1

We have to find number of trials , that is sample size n.

Formula:
n=px (1 - p) x N19

Zc is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

. | 0.0 10.1 10.2 10.3 0.4 | 0.5 0.6 0.7 0.8 0.9 .01 .5040 5438 .5832 .6217 6591 6950 .02 .5080 5478 .5871 .6255 .6628 .6985

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Zc = 1.645

Thus

n=px (1 - p) x N19

n=0.4 x (1 – 0.4) X / 1.645 0.1

n = 0.4 x 0.6 X (16.45)

n = 0.24 x 270.6025

n = 64.9446

n = 65

Thus required number of trials are: 65

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