Normal distributions

Question 1

What kinds of variable can normal distributions be used for?

Answer 1

Continuous (eg. height, weight, length)

Question 2

What do both discrete and continuous probability distributions sum to?

Answer 2

Must all ad to 1, so area under normal dist. = 1

Question 3

In normal dist. how do you calc probability between 2 bounds?

Answer 3

Calculate the area under the graph between them

Question 4

For a normal dist. what is the. probability of X being exactly equal to something?

Answer 4

0, since area under graph would be so slim and small

Question 5

How much of normal dist area lies in 𝜎, 2𝜎 and 3𝜎 respectively?

Answer 5

68% in 𝜎, 95.5% in 2𝜎 and 99.7% in 3𝜎

Question 6

What is meant by a normal dist. being symmetrical?

Answer 6

Mean = median = mode

Question 7

in a normal dist, what does 𝜎 and 𝜇 mean?

Answer 7

standard deviation and mean respectively

Question 8

How is a normal distribution denoted?

Answer 8

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

Note when inputting into dist calc, sq.rt Variance and put in standard deviation instead

Question 9

What to watch out for in normal dist Qs?

Answer 9

There may be a binomial question at the end you need to unravel.

Question 10

When can a normal dist. be used to approximate a binomial dist. ?

Answer 10

When n (sample size) is large and when p is close to 0.5 (so that the dist will be symmetrical like a normal dist)

Question 11

How do you convert Binomial dist to normal dist (given in formula book)?

Answer 11

Use probability X sample size to find mean (𝜇) and then mean X (1 - p) to give variance (𝜎²) which can then be square rooted to find std. dev..
can be combined to form:
X ~ N(𝜇,𝜎²)

Question 12

When is a continuity correction required?

Answer 12

When going from a discrete variable (Ie. Binomial) to a continuous variable (Ie. normal)

Question 13

What is a continuity correction?

Answer 13

Question 14

How do you do a continuity correction?

Answer 14

When looking at bounds, if asking for
X ≤ x or X ≥ x, add 0.5 or subtract it respectively so that the actual number is included within the region.
If asking for X < x or X > x, subtract 0.5 or add it respectively
(X is value being asked to find, x is just a given number

Question 15

How do you run a hypothesis test on a sample mean?

Answer 15

Identify population mean (𝜇), sample size (n), std. dev. (𝜎) and sample mean x̄ .
State H₀ as 𝜇 = pop. mean and H₁ as 𝜇 does not equal pop mean (can be in a particular dir.)
Use 𝜎/√n to give s.d of sample
Formulate 𝜇 and new sd into a normal model and use calc. to find probability of x being >/< x̄
if this is less than sig level, reject H₀ as null hypothesis incorrect

Question 16

How do you find critical values on a sample mean?

Answer 16

carry out a normal Hyp test for this then when it comes to inputting a sample mean (which you won’t have) input sig level in prob parameter (on dist graph page) for either greater or less than
For 2 tailed tests, do 1-sig level and put it into prob parameter for p(a<X<b) - this will give crit. values at both ends.