Respuesta :
Answer:
Step-by-step explanation:
[tex]M = (5 + 0 + 4 + 5 + 1 + 2 + 4) / 7 = 3\\[/tex][tex]Variance = [(5-3)^2 + (0-3)^2 + (4-3)^2 + (5-3)^2 + (1-3)^2 + (2-3)^2 + (4-3)^2] / 7 = 2.857\\\\standard deviation\\\sqrt{\frac{(0-3)^2 + (4-3)^2 + (5-3)^2 + (1-3)^2 + (2-3)^2 + (4-3)^2] }{7}} \\=1.69[/tex]
b. Find the z-score for each score in the sample.
The z-score is a measure of how many standard deviations an element is from the mean. It is calculated using the formula:
z = (X - M) / s
where X is the score, M is the mean, and s is the standard deviation.
Here are the z-scores for each score in the sample:
For X = 5: z = (5 - 3) / 1.69 = 1.18
For X = 0: z = (0 - 3) / 1.69 = -1.78
For X = 4: z = (4 - 3) / 1.69 = 0.59
For X = 1: z = (1 - 3) / 1.69 = -1.18
For X = 2: z = (2 - 3) / 1.69 = -0.59
c. Transform the original sample into a new sample with a mean of M = 50 and s = 10.
To transform the original sample into a new sample with a mean of M = 50 and s = 10, you can use the following formula:
New X = (Old X - Old M) * (New s / Old s) + New M
Here are the transformed scores:
For Old X = 5: New X = (5 - 3) * (10 / 1.69) + 50 = 61.83
For Old X = 0: New X = (0 - 3) * (10 / 1.69) + 50 = 32.25
For Old X = 4: New X = (4 - 3) * (10 / 1.69) + 50 = 55.92
For Old X = 1: New X = (1 - 3) * (10 / 1.69) + 50 = 38.17
For Old X = 2: New X = (2 - 3) * (10 / 1.69) + 50 = 44.08
