A populations of scores forms a normal distribution with a mean of 40 and a standard deviation of 12 what is the probability of selecting a sample of n=9 scores with a mean less than m=34
To answer this question, we need to use the properties of the normal distribution and the concept of sampling. Here are the steps to calculate the probability:
Step 1: Standardize the sample mean:
We need to calculate the z-score for the sample mean using the formula:
z = (sample mean - population mean) / (population standard deviation / square root of the sample size)
In this case:
sample mean (m) = 34,
population mean (μ) = 40,
population standard deviation (σ) = 12, and
sample size (n) = 9.
So the z-score would be:
z = (34 - 40) / (12 / sqrt(9))
Step 2: Look up the z-score in the standard normal distribution table:
We need to find the area/probability to the left of the z-score we calculated in Step 1 in the standard normal distribution table.
Step 3: Calculate the probability:
Once you find the z-score in the table, you will get a corresponding probability. This probability represents the area under the normal curve to the left of the calculated z-score.
That probability is the answer to the question and it represents the probability of selecting a sample of n=9 scores with a mean less than m=34.
Remember, the standard normal distribution table provides the probabilities for z-scores. If the table does not include the exact z-score, round it to the nearest value and use the corresponding probability.