The normal distribution

Question 1

How is a normally distributed variable notated?

Answer 1

X∼N(µ,σ²), where µ is the mean and σ² is the variance

Question 2

How is the standard normal variable notated?

Answer 2

Z

Question 3

How is the standard normal variable distributed?

Answer 3

Z∼N(0,1)

Question 4

How is P(Z≤z) notated?

Answer 4

ϕ(z)

Question 5

What is P(Z≥z) equal to?

Answer 5

1-ϕ(z)

Question 6

What is P(Z≤-z) equal to?

Answer 6

1-ϕ(z)

Question 7

What is P(z₁≤Z≤z₂) equal to?

Answer 7

ϕ(z₂)-ϕ(z₁)

Question 8

For a variable X∼N(µ,σ²), how can P(X≤x) be calculated?

Answer 8

ϕ((x-µ)/σ)