Answer:

And we can use the z score formula given by:

And if we find the parameters we got:


And we can find the z score for the value of 0.4 and we got:

And we can find this probability:

And if we use the normal standard table or excel we got:

Step-by-step explanation:
For this case we have the following info given:
represent the proportion of the company's orders come from first-time customers
represent the sample size
And we want to find the following probability:

And we can use the normal approximation since we have the following two conditions:
1) np = 158*0.26 = 41.08>10
2) n(1-p) = 158*(1-0.26) = 116.92>10
And for this case the distribution for the sample proportion is given by:

And we can use the z score formula given by:

And if we find the parameters we got:


And we can find the z score for the value of 0.4 and we got:

And we can find this probability:

And if we use the normal standard table or excel we got:
