A carpet expert believes that 8% of Persian carpets are counterfeits. If the expert is accurate, what is the probability that the proportion of counterfeits in a sample of 827 Persian carpets would be greater than 7%

And we can use the normal standard distribution table and  the cmplement rule and we got:

Step-by-step explanation:

For this case we know the following info given:

represent the population proportion

represent the sample size selected

We want to find the following proportion:

For this case we can use the normal approximation since we have the following conditions:

i) np = 827*0.08 = 66.16>10

ii) n(1-p) = 827*(1-0.08) =760.84>10

The distribution for the sample proportion would be given by:

The mean is given by:

And the deviation:

We can use the z score formula given by:

And replacing we got:

And we can use the normal standard distribution table and  the cmplement rule and we got: