In: Statistics and Probability
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.
Solution:
Given that,
n = 487
= 7% =0.07
1 - = 1 - 0.07 = 093
= = 0.07
= ( 1 - ) / n
= 0.07 * 0.93 / 487
= 0.0116
= 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