Question

In: Statistics and Probability

A telephone exchange operator assumes that 7% of the phone calls are wrong numbers. Step 1...

A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.

Step 1 of 1:

If the operator is right, what is the probability that the proportion of wrong numbers in a sample of 487 phone calls would differ from the population proportion by more than 3% ? Round your answer to four decimal places.

Expert Solution

Solution:

Given that,

n = 487

= 7% =0.07

1 - = 1 - 0.07 = 093

= = 0.07

= $\sqrt$ ( 1 - ) / n

= $\sqrt$ 0.07 * 0.93 / 487

= 0.0116

P( > 0.03 )

1 - P ( 0.04 < < 0.10 )

1 -P ( 0.04 - 0.07 / 0.0116 ) < ( - / ) < ( 0.10 - 0.07 / 0.0116 )

1 -P ( - 0.03 / 0.0116 < z < 0.03 / 0.0116 )

1 - P (-2.59 < z < 2.59 )

1 - P ( z < 2.59) - p ( z < -2.59 )

Using z table

= 1 - ( 0.9952 - 0.0048)

= 1 - 0.9904

= 0.0096

Probability = 0.0096

orchestra answered 2 years ago

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