Year 2 - Chapter 3 w/ The Normal Distribution

Question 1

What are the properties of a bell-curved graph?

Answer 1

✯ Has a bell-shaped curve.
✯ Symmetrical about the mean.
✯ Mean = Mode = Median for a normal distribution.
✯ Area under curve represents probability (adds up to 1).

Question 2

At which point does the point of inflection on a normal distribution curve occur at?

Answer 2

μ + or - σ

Question 3

How much of the data is within one standard deviation of the mean?

Answer 3

68%

Question 4

How much of the data is within two standard deviations of the mean?

Answer 4

95%

Question 5

How much of the data is within three standard deviations of the mean?

Answer 5

99.7%

Question 6

Suppose we have a normal distribution

X ~ N (μ, σ^2)

When standardised, what does the distribution look like?

Answer 6

X ~ Z (0,1)

Question 7

How else can P (Z<z) be represented?

Answer 7

Φ (z)

Question 8

How can we find z?

Answer 8

X-μ/σ

or..

Use the percentages point table when given P(Z > z) = p

Question 9

When can standardise a normal distribution?

Answer 9

We can standardise a normal distribution when an unknown must be find (such as μ)

Question 10

What two conditions need to be met when approximating the binomial distribution?

Answer 10

1. N has to be large (>50)
2. P has to be close to 0.5

N is the number of trials
P is the fixed probability of success.

Question 11

When approximating the binomial distribution, how can we find μ and σ?

Answer 11

μ = n x p = np

σ = √(np)(1-p)

Question 12

What are the seven steps needed for hypothesis testing with the normal distribution?

Answer 12

1. Define variable
2. Write normal distribution
3. Write down ND with sample mean.
4. Write hypothesis (H0, H1)
5. Calculate probability
6. Choose to accept or reject hypothesis
7. Conclusion in context.

Question 13

What must we always do when dealing with normal approximation w/ binomials?

Answer 13

CONTINUITY CORRECTION!