Answer:
The standard error of the mean is 0.0783.
Step-by-step explanation:
The Central Limit Theorem helps us find the standard error of the mean:
The Central Limit Theorem estabilishes that, for a random variable X, with mean
and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
.
The standard deviation of the sample is the same as the standard error of the mean. So

In this problem, we have that:

So



The standard error of the mean is 0.0783.
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Given:
Do you earn over $50,000 per year?
Male Female Total
Income over 50,000 475 375 850
Income below 50,000 75 75 150
Total 550 450 1,000
Yes, "being female" and "earning over 50,000" are independent events. Independents events are events that happen where the probability of one event happening is not affected by the happening of the other event.
In this case, regardless if you are male or female, you can earn over 50,000.
Also if you are female, you either earn under or over 50,000