Normal Distribution - [Statistics 2].

Question 1

How do you write a Normal Distribution?

Answer 1

X~N(μ, σ²).

μ = Mean.
σ² = Variance.

Question 2

What shape is a Normal Distribution Graph?

Answer 2

A Bell-Shaped Curve where there is the largest area in the middle and smallest sections on the outside.

Question 3

What percentage of values lie within 1 standard deviation of the mean?

For a Normal Distribution?

What else lies 1 S.D away from the mean?

Answer 3

2/3 (67%).

Points of Inflection.

Question 4

What percentage of values lie within 2 standard deviation of the mean?

Answer 4

95%.

Question 5

What percentage of values lie within 3 standard deviation of the mean?

Answer 5

99.8%.

Question 6

How do you calculate x̄ from ∑x, ∑(x-x̄)² and n?

Answer 6

x̄ = ∑x / n.

Question 7

How do you calculate the Standard Deviation from ∑x, ∑(x-x̄)² and n?

Answer 7

S.D = √(∑(x-x̄)²) / n.

Question 8

What things do you need to write to explain why you can use a Normal Distribution?

Answer 8

• The Data is Symmetrical.
• The Data is Continuous.
• Most of the Data lies in the middle.

Question 9

What equation allows you to Standardise the vales of X to Z?

Answer 9

Z = X - μ / σ.

Question 10

If P(Z < z) = 0.5, what is the Area, Tail, μ and σ to use in InvN, given that Z~N(0, 1²)?

Answer 10

• Area = 0.5.
• Tail = Left Tail.
• μ = 0.
• σ = 1.

Question 11

If σ² = Variance, then what does Standard Deviation equal?

Answer 11

S.D = σ = √σ² = √Variance.

Question 12

When can a Normal Distribution be used to approximate a Binomial Distribution?

Answer 12

• When ‘n’ is large (n ≥ 20) and p ≈ 0.5.
  OR
• np ≥ 5 and n(1-p) ≥ 5.