Suppose that 20% of all invoices are for amounts greater than $1, 000. A random sample of 60 invoices is taken. What is the probability that the proportion of invoices in the sample is less than 18%?

34.83% probability that the proportion of invoices in the sample is less than 18%

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

For a proportion p in a sample of size n, we have that

In this problem, we have that:

So

What is the probability that the proportion of invoices in the sample is less than 18%?

This is the pvalue of Z when X = 0.18. So

has a pvalue of 0.3483

34.83% probability that the proportion of invoices in the sample is less than 18%

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8