Normal distribution

Normal Distribution

a) Normal Distribution

a) Normal Distribution

a) Normal Distribution

a) Normal Distribution

a) Normal Distribution

Multiple Choice

Given that:

μ = 56 and σ = 7

Find the standardized score for a raw score of 70.

• z = 0

• z = 1.5

• z = –0.5

• z = 2

Multiple Choice

Given that:

μ = 56 and σ = 7

Find the standardized score for a raw score of 52.5.

• z = 0

• z = 1.5

• z = –0.5

• z = 2

Multiple Choice

Given that:

μ = 56 and σ = 7

Find the standardized score for a raw score of 66.5.

• z = 0

• z = 1.5

• z = –0.5

• z = 2

Multiple Choice

Given that:

μ = 56 and σ = 7

Find the standardized score for a raw score of 56.

• z = 0

• z = 1.5

• z = –0.5

• z = 2

Multiple Choice

Given that:

μ = 56 and σ = 7

Find the a raw score for standardized score of 1.3.

• x = 65.1

• x = 39.2

• x = 53.2

• x = 70

Multiple Choice

Given that:

μ = 56 and σ = 7

Find the a raw score for standardized score of –2.4.

• x = 65.1

• x = 39.2

• x = 53.2

• x = 70

Multiple Choice

Given that:

μ = 56 and σ = 7

Find the a raw score for standardized score of –0.4.

• x = 65.1

• x = 39.2

• x = 53.2

• x = 70

Multiple Choice

Given that:

μ = 56 and σ = 7

Find the a raw score for standardized score of 2.0.

• x = 65.1

• x = 39.2

• x = 53.2

• x = 70

b) Standard Normal Distribution

b) Standard Normal Distribution

b) Standard Normal Distribution

b) Standard Normal Distribution

b) Standard Normal Distribution

b) Standard Normal Distribution

​If Z ~ N(0, 1²) find P(Z < 0.247).

​P(Z < 0.247) = 0.5948 + 0.0027 = 0.5975

Multiple Choice

If Z ~ N(0, 1²) find Φ(1.62).

[Hint: P(Z < 1.62) = Φ(1.62)]

• 0.9474

• 0.2236

• 0.0934

• 0.8438

Multiple Choice

If Z ~ N(0, 1²) find P(Z > 0.76).

[Hint: P(Z > 0.76) = 1 – Φ(0.76)]

• 0.9474

• 0.2236

• 0.0934

• 0.8438

Multiple Choice

If Z ~ N(0, 1²) find P(Z < –1.32).

[Hint: P(Z < –1.32) = 1 – Φ(1.32)]

• 0.9474

• 0.2236

• 0.0934

• 0.8438

Multiple Choice

If Z ~ N(0, 1²) find P(–1.2 < Z < 1.738).

[Hint: P(–1.2 < Z < 1.738) = Φ(1.738) – Φ(–1.2)]

• 0.9474

• 0.2236

• 0.0934

• 0.8438

b) Standard Normal Distribution

​If X ~ N(2, 5²) find P(X < 7).

b) Standard Normal Distribution

​If X ~ N(2, 5²) find P(X > 11).

b) Standard Normal Distribution

​If X ~ N(2, 5²) find P(|X| < 3).

b) Standard Normal Distribution

​If X ~ N(2, 5²) find P(|X - 2| < 6).

b) Standard Normal Distribution

​If X ~ N(2, 5²).

Find x such that P(X > x) = 0.05