Suppose 47% of the population has a college degree. If a random sample of size 780 is selected, what is the probability that the proportion of persons with a college degree will be less than 44%? Round your answer to four decimal places.

0.0465 = 4.65% probability that the proportion of persons with a college degree will be less than 44%

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

The standard deviation of the binomial distribution is:

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that , .

In this problem, we have that:

So

What is the probability that the proportion of persons with a college degree will be less than 44%?

This is the pvalue of Z when X = 0.44*780 = 343.2. So

has a pvalue of 0.0465

0.0465 = 4.65% probability that the proportion of persons with a college degree will be less than 44%

step-by-step explanation:

a rhombus is a parallelogram enjoying his symmetry.