Question

The weight of baby elephants is believed to be Normally distributed, with a mean of 123.5 pounds. The average weight of a random sample of 35 baby elephants is found to be 125.7 pounds, with a standard deviation of 11.3 pounds. What is the standard error of the mean

Answer 1

Answer:

The standard error of the mean is 1.91 pounds.

Step-by-step explanation:

We are given that the weight of baby elephants is believed to be Normally distributed, with a mean of 123.5 pounds. The average weight of a random sample of 35 baby elephants is found to be 125.7 pounds, with a standard deviation of 11.3 pounds.

which means, $\bar X$ = sample mean = 125.7 pounds

                       $\sigma$ = standard deviation = 11.3 pounds

                       $\mu$ = population mean = 123.7 pounds

                      n = random sample = 35

Now, the Central Limit Theorem states that, for a any normally distributed random variable X, with given mean and standard deviation, the standard error of the mean, is given by;

            Standard error = $\frac{\sigma}{\sqrt{n} }$

So, here $\sigma$ = 11.3 and n = 35

Hence, Standard error = $\frac{11.3}{\sqrt{35} }$ = 1.91 pounds

Therefore, the standard error of the mean is 1.91 pounds.

Answer 2

Answer:

The standard error of the mean is 1.91 pounds

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation, which is also called standard error of the mean, is $s = \frac{\sigma}{\sqrt{n}}$

In this problem we have that:

$\sigma = 11.3, n = 35$

So

$s = \frac{11.3}{\sqrt{35}} = 1.91$

The standard error of the mean is 1.91 pounds