Normal Distribution

Question 1

What does the area under the normal distribution equal?

Answer 1

1

Question 2

What % of values lie in 1 σ of the µ

Answer 2

68% lie in µ +- σ

Question 3

What % of values lie in 2σ of µ

Answer 3

95% lie in µ +- 2σ

Question 4

What % of values lie in 3σ of µ

Answer 4

99.7% lie in µ +- 3σ

Question 5

Where do the points of inflection lie on a normal distribution?

Answer 5

µ +- σ

Question 6

How do you convert between a value in a normal distribution (X) to the standard normal (Z)?

Answer 6

Z = (X-µ)/σ

So Z is measuring how many standard deviations from the mean it is

Question 7

What are the characteristics needed for a binomial to be modelled with the normal distribution?

Answer 7

1. The probability of n”success” needs to be close to 0.5 (0.4 <= p <= 0.6)
2. The number of trials is large (n >= 50)

Question 8

How do you find the mean if you are modelling binomial with normal?

Answer 8

µ = np (n is number of trials and p is probability of success)

Question 9

How do you find the standard deviation if you are modelling binomial with normal?

Answer 9

σ = sqrt(np(1-p))

Question 10

Why is useful to approximate binomials with normal?

Answer 10

Calculating binomials can be processing intensive and normal is quicker and easier

Question 11

What must you always remember to do if you are finding a specific probability in a normal approximation of a binomial?

Answer 11

CONTINUITY CORRECT

so if the binomial is P(X>=7) for normal that’s P(Y>=6.5)

Question 12

What is the sample mean distributed around?

Answer 12

The population mean

Question 13

What is the variance of a random sample?

Answer 13

σ^2/n

Question 14

Equation to convert a sample mean value to a standard normal value

Answer 14

Z = (x-µ) / (σ/n)

Question 15

What is required when calculating the standard deviation of sample means from the standard deviation of a sample?

Answer 15

The sample needs to be large (over 30)

Question 16

What do you need to do to the significance level when doing a two tailed normal hypothesis test?

Answer 16

Divide the size of the critical region by two