Question

A population consists of the following scores:

6 12 19 47 32 33 8 8 9 23

1. Compute the μ and the σ for the population.

2. On a horizontal axis under the bell curve, plot the μ, the σ, and the values for the SD lines. Then record the raw scores in the table on the Template.

3. Find the z-score for each score in the population, plot the z-score  μ, the σ, and the values for the SD lines, and plot them on the horizontal axis under the bell curve.

4. Record the z scores in the table on the Template.

5. Transform the original population into a new population of T-scores with a μ = 50 and a σ = 10, plot the new μ, the σ, and the values for the SD lines on the horizontal axis under the bell curve,

6. Record the T scores in the Table on the Template.

7. Describe the shape of the distribution.

Answer 1

1. Enter data in excel.

By using excel function =AVERAGE(data range):

By using excel function =STDEV.P(data range):

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2. The values for the SD lines

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3 and 4. The z score can be calculated by using formula:

6	-1.04
12	-0.59
19	-0.05
47	2.08
32	0.94
33	1.01
8	-0.89
8	-0.89
9	-0.82
23	0.25

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5.

Data	z	T=10Z+50
6	-1.04	39.6
12	-0.59	44.1
19	-0.05	49.5
47	2.08	70.8
32	0.94	59.4
33	1.01	60.1
8	-0.89	41.1
8	-0.89	41.1
9	-0.82	41.8
23	0.25	52.5

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6.

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7. The shape of the distribution is approximately normal.