I cant figure this out!!!

The income of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. If a sample of 100 trainees is selected, what is the probability that the sample mean will be less than $1075 month?

The standard error (SE) of the mean is the standard deviation (SD) divided by the square root of the number in the sample.

In this case, your Z score would be ($1075-$1100)/SE. Find the Z score and look it up in the back of your statistics text in a table labeled something like "areas under the normal disrtibution."

I hope this helps. Thanks for asking.

Still don't get it...sorry. I am really trying to get it without asking for the answer, but I just don't get it. Help please.....

Your SE = SD/sq.root of n

SE = 150/10 = 15

For a distribution of sample means, the Z score = (1075-1100)/15.

Can you calculate the Z score and use it in the table to find the probability?

I hope this helps a little more. Thanks for asking.

To find the probability that the sample mean will be less than $1075 per month, we can make use of the Central Limit Theorem (CLT). According to the CLT, when a large enough sample size is taken from a population, the distribution of the sample means will be approximately normally distributed, regardless of the distribution of the population.

Here's how we can solve this problem step by step:

Step 1: Find the mean of the sample means.
The mean of the population is given as $1100, which will also be the mean of the sample means since the sample means follow the same distribution.

Step 2: Find the standard deviation of the sample means.
The standard deviation of the sample means, also known as the standard error, can be calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population standard deviation is $150, and the sample size is 100.

Standard Error (SE) = Population Standard Deviation / sqrt(Sample Size)
SE = $150 / sqrt(100)
SE = $150 / 10
SE = $15

Step 3: Standardize the sample mean.
To use the normal distribution table, we need to standardize the sample mean. We do this by subtracting the mean of the sample means from the desired value and dividing it by the standard error.

z = (Sample Mean - Mean of Sample Means) / Standard Error
z = ($1075 - $1100) / $15
z = -25 / $15
z = -1.67

Step 4: Find the probability using the standard normal distribution table.
Now that we have standardized the sample mean, we can use the standard normal distribution table to find the probability of getting a z-score of -1.67 or less. Using the table or a calculator, we find that the probability is approximately 0.0475.

Therefore, the probability that the sample mean will be less than $1075 per month is approximately 0.0475.