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Helga [31]
3 years ago
6

The weight of baby goats is believed to be Normally distributed, with a mean of 5.75 pounds. The average weight of a random samp

le of 20 baby goats is found to be 6.15 pounds, with a standard deviation of 0.35 pound. What is the standard error of the mean
Mathematics
1 answer:
Julli [10]3 years ago
7 0

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 \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

The standard deviation of the sample is the same as the standard error of the mean. So

SE_{M} = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\sigma = 0.35, n = 20

So

SE_{M} = \frac{\sigma}{\sqrt{n}}

SE_{M} = \frac{0.35}{\sqrt{20}}

SE_{M} = 0.0783

The standard error of the mean is 0.0783.

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