Question

Given the data set (10, 8, 6, 4, 7, 5), what will be the z-score values when this is converted to a standard normal distribution? (Hint: use the population standard deviation).

Options:
A) (1.69, 0.68, -0.34, -1.36, 0.17, -0.85)
B) (3.33, 1.33, -0.67, -2.67, 0.33, -1.67)
C) (11.09, 1.77, 0.45, 7.13, 0.11, 2.79)
D) None of the above

Answer 1

To convert the given data set to a standard normal distribution, you need to calculate the mean and standard deviation of the data set and then calculate the z-score for each data point. Hence correct option is d. "None of the above".

Step-by-step explanation:

To convert the given data set (10, 8, 6, 4, 7, 5) to a standard normal distribution using the population standard deviation, we can follow these steps:

1. Calculate the mean of the data set, which is (10+8+6+4+7+5)/6 = 6.
2. Calculate the standard deviation of the data set using the population formula. The population standard deviation is the square root of the variance, which is ((10-6)^2 + (8-6)^2 + (6-6)^2 + (4-6)^2 + (7-6)^2 + (5-6)^2)/6 = 2.8.
3. For each data point, calculate the z-score by subtracting the mean from the data point and dividing by the standard deviation. The z-scores for the given data set are: (10-6)/2.8 = 1.43, (8-6)/2.8 = 0.71, (6-6)/2.8 = 0, (4-6)/2.8 = -0.71, (7-6)/2.8 = 0.36, and (5-6)/2.8 = -0.36.

Therefore, the correct z-score values when the data set is converted to a standard normal distribution are (1.43, 0.71, 0, -0.71, 0.36, -0.36). Hence correct option is d. "None of the above".