Question

determine the standard error. multiple choice 4 points if the standard deviation of a population is 20 and we take a sample of size 16 from which to calculate a mean, the standard error (the standard deviation of the sample mean) is: 1.25 2.5 5 10 20
find the indicated probability. multiple choice 4 points the average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (source: american dietetic association). if a sample of 50 individuals is randomly selected, find the probability that the mean of the sample will be less than 200 pounds. 0.0985 0.8815 0.9015 0.7613

Explanation:

Step 1: Recall the formula for standard error

The formula for the standard error ($SE$) of the mean is $SE=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard - deviation and $n$ is the sample size.

Step 2: Identify the values of $\sigma$ and $n$

Given that $\sigma = 20$ and $n = 16$.

Step 3: Calculate the standard error

Substitute the values into the formula: $SE=\frac{20}{\sqrt{16}}=\frac{20}{4}=5$.

for question 23:

Step 1: Identify the mean and standard - deviation of the sampling distribution of the sample mean

The mean of the sampling distribution of the sample mean $\mu_{\bar{x}}=\mu = 196$ and the standard deviation of the sampling distribution of the sample mean (also known as the standard error) $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma = 22$ and $n = 50$. So, $\sigma_{\bar{x}}=\frac{22}{\sqrt{50}}\approx\frac{22}{7.071}\approx3.111$.

Step 2: Calculate the z - score

The z - score is calculated using the formula $z=\frac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}$. We want to find $P(\bar{X}<200)$, so $z=\frac{200 - 196}{3.111}=\frac{4}{3.111}\approx1.29$.

Step 3: Find the probability using the z - table

Looking up the z - value of 1.29 in the standard normal distribution table, we find that $P(Z < 1.29)=0.9015$.

Answer:

5