Question

Show all work please.

1. Certain standardized math exams have a mean of 100 and a standard deviation of 60. Of a sample of 36 students who take this exam, what percent could you expect to score between 70 and 110?

A) 84

B) 81.5

C) 83.85

D) 85

2. Certain standardized math exams had a mean of 120 and a standard deviation of 20. Of students who take this exam, what percent could you expect to score between 60 and 80?

A) 2.5

B) 2.35

C) 97.5

D) 13.5

3. A random sample of n measurements was selected from a population with unknown mean μ and known standard deviation σ. Using the 68-95-99.7 rule, calculate a 68% confidence interval for μ for the given situation. Round to the nearest hundredth when necessary.
n = 100, Xbar = 74, σ = 25

A)		74 ± 0.49
B)		74 ± 2.5
C)		74 ± 25
D)		74 ± 2.10

4.Certain standardized math exams have a mean of 100 and a standard deviation of 60. Of a sample of 36 students who take this exam, what percent could you expect to score above 90?

A)84

B)81.5

C)83.85

D)16

Answer 1

Solution:-

1) The percent could you expect to score between 70 and 110 is 84% .

Mean = 100, S.D = 60, n = 36

x₁ = 70

x₂ = 110

By applying normal distribution:-

z₁ = - 3.0

z₂ = 1.0

P( -3.0 < z < 1.0) = P(z > - 3.0) - P(z > 1.0)

P( -3.0 < z < 1.0) = 0.9987 - 0.1587

P( -3.0 < z < 1.0) = 0.84

P( -3.0 < z < 1.0) = 84%

2) (B) The percent could you expect to score between 60 and 80 is 2.35.

Mean = 120, S.D = 20

x₁ = 60

x₂ = 80

By applying normal distribution:-

z₁ = - 3.0

z₂ = - 2.0

P( -3.0 < z < -2.0) = P(z > - 3.0) - P(z > -2.0)

P( -3.0 < z < -2.0) = 0.9987 - 0.9772

P( -3.0 < z < -2.0) = 0.0215