Statistics - Normal

Question 1

What is the normal distribution?

Answer 1

Continuous probability distribution

Question 2

What is the area under the curve of the normal distribution?

Answer 2

1

Question 3

What is the notation for a normal distribution?

Answer 3

X~N(μ,σ^2)
μ - mean
σ^2 - varience
σ - standard dev

Question 4

What is the shape of the normal distribution?

Answer 4

Bell-shaped curve with asymptotes at each end

Question 5

How is the normal distribution symmetrical?

Answer 5

Symmetrical about x = μ

mean = mode = median

Question 6

Where are the points of inflection on the normal distribution?

Answer 6

μ + σ AND μ-σ

Question 7

What is σ?

Answer 7

Standard deviation

Question 8

What % of data lies within 1 standard deviation of mean?

Answer 8

Approx 68%

Question 9

What % of data lies within 2 standard deviations of the mean?

Answer 9

Approx 95%

Question 10

What % of data lies within 3 standard deviations of the mean?

Answer 10

Nearly all

Question 11

What is the upper/lower when only one boundary given?

Answer 11

If lower boundary given, the upper is 5*σ + mean

If upper boundary given, the lower is mean - 5*σ

Question 12

Why can you use >/< instead of >= / <= ?

Answer 12

No difference as its a continuous normal distribution

Question 13

What is the standard normal distribution?

Answer 13

Normal distribution is when
μ = 0
σ = 1

Question 14

How is the standard normal distribution shown?

Answer 14

Z~N(0,1^2)

Question 15

What is the coding for standard normal distribution?

Answer 15

Z = (X-μ) / σ

Question 16

What should be done if the probability to the right is given with a standard value (top %)?

Answer 16

Use percentage points table

Question 17

When can you approx the normal from a binomial distribution?

Answer 17

n is large (above 50)

p is close to 0.5

Question 18

How do you calculate μ & σ from binomial when approximating?

Answer 18

μ = np
σ = √(np-n*p^2) = √(μ*(1-p))

Question 19

What is continuity correction?

Answer 19

Probabilities are discrete in binomial

When approximating to normal you must correct to make it continuous

Question 20

How do you continuity correct a variable that is less than or equal to 70?

Answer 20

Use values less than 70.5

Question 21

What is the sample mean of a sample size n taken from a normally distributed sample X?

Answer 21

x̄~N(μ, σ^2/2)

Question 22

What is the Z value when coding a sample mean?

Answer 22

Z = X-μ/ (σ/√n)