Question

(Q27-32)The scores of Business Analytics I follow approximately the Normal distribution with mean μ=70 and standard deviation σ = 10.  

When the score is 80, what is the corresponding Z value?

		-1
		1
		10
		-10

What proportion all students who take the Business Analytics I score 80 or more?

		0.8413
		0.68
		0.1587
		0.32

What is the probability that students score between 80 and 90?

		0.9772
		0.0228
		0.8413
		0.1359

When a student places in the top 1%, what is the corresponding Z value?

		2.4
		2.33
		-2.33
		-2.4

How high must a student score to place in the top 1%?

		92
		93.3
		95
		97

How high must a student score to place in the top 10% of all students taking the Business Analytics I?

		78
		82
		82.8
		92

Answer 1

Solution :

Given that,

mean = = 70

standard deviation = = 10

27 ) x = 80

Using z-score formula,

z = x - /  

= 80 - 70 /10

= 10 / 10

= 1

z = 1

28 ) P (x > 80)

= 1 - P (x < 80 )

= 1 - P ( x -  / ) < ( 80 - 70 / 10)

= 1 - P ( z < 10 / 10 )

= 1 - P ( z < 1 )

Using z table

= 1 - 0.8413

= 0.1587

Probability = 0.1587

option 0.1587 is correct

28 ) P (80 < x < 90 )

P ( 80 - 70 / 10) < ( x -  / ) < ( 90 - 70 / 10)

P ( 10 / 10 < z < 20 / 10 )

P (-1 < z < 2)

P ( z < 2 ) - P ( z < 1)

Using z table

= 0.9772 - 0.8413

= 0.1359

Probability = 0.1359

Option 0.1359 is correct.

30 ) P( Z > z) = 1%

P(Z > z) = 0.01

1 - P( Z < z) = 0..01

P(Z < z) = 1 - 0.01

P(Z < z) = 0.99

z = 2.33

option 2.33 is correct

31 ) Using z-score formula,

x = z * +

x = 2.33* 10 + 70

x = 78

32) P( Z > z) = 10%

P(Z > z) = 0.10

1 - P( Z < z) = 0..10

P(Z < z) = 1 - 0.10

P(Z < z) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28* 10 + 70

x = 82.8

Option 82.8 is correct.