Question

3. A population of scores has µ = 44. In this population, a score of X = 40 corresponds to z = –0.50. What is the population standard deviation?​

	a.	2​
	b.	​4
	c.	​8
	d.	​-8

4. Last week Tim got a score of X = 54 on a math exam with µ = 60 and σ = 8. He also got X = 49 on an English exam with µ = 55 and σ = 3, and he got X = 31 on a psychology exam with µ = 37 and σ = 4. For which class should Tim expect the best grade?​ Hint: Be sure to consider if you are above the mean or below the mean…then sketch each distribution using the data given for each class. ​

	a.	​Math
	b.	​English
	c.	​Psychology
	d.	​All 3 grades should be the same.

Answer 1

Answer:

3.

To give the standard deviation

Given,

Mean = 44

X = 40

z = - 0.50

Consider,

z = (x - mu)/s

substitute known values

- 0.50 = (40 - 44)/s

s = (40 - 44)/(-0.50)

= (-4) / (-0.50)

= 8

Standard deviation = 8

Option C is right answer.

4.

Consider,

Maths score z = (x - mu)/s

substitute values

= (54 - 60)/8

= -6/8

z = - 0.75

English score z = (x - mu)/s

substitute values

= (49 - 55)/3

= - 6/3

z = - 2

Psychology score z = (x - mu)/s

substitute values

= (31 - 37)/4

z = - 1.5

So here by observing the scores we can say that tim score best grade in maths.

i.e.,

Option A