Normal Distribution

Question 1

What is the notation for a normal distribution?

Answer 1

X ~ N ( µ, σ² )

Question 2

What can be said of the bell curve for normal distribution?

Answer 2

• It is symmetrical (mean = median = mode)
• Total area under the curve = 1 (probability)

Question 3

When should you use the inverse normal distribution?

Answer 3

When given the probability of a value being greater than / less than another

Question 4

P( X > a) = 0.4, how should you label the bell curve?

Answer 4

A shaded area of 0.6 for X < a

Question 5

What does the inverse normal function calculate the probability of?

Answer 5

X < …..

Question 6

What does normal pd find?

Answer 6

The probability X = a

Question 7

What does normal cd find?

Answer 7

The probability X < a

Question 8

How do you find the interquartile range of a normal distribution?

Answer 8

• Upper limit 75%
• Lower limit 25%
• Find critical value at 75% using inverse normal and do the same for the critical value at 25%
• Subtract values to give IQR

Question 9

What should you use as the lower limit for a standardised normal distribution?

Answer 9

-999 not 0

Question 10

When do you use the standard normal distribution?

Answer 10

To find σ & µ if they are unknown

Question 11

What is the standard deviation and mean for a standard normal distribution?

Answer 11

Mean = 0
Standard deviation = 1

Question 12

What is the formula for converting standard normal data to normal data ( z -> x)?

Answer 12

z = (x - µ)/σ

Question 13

What are the steps for finding σ / µ?

Answer 13

• Standard normal
• Inverse normal
• Use z/x formula

Question 14

How do you draw the standard normal distribution?

Answer 14

Use the area given in the question and label up the mean as 0 and the standard deviation and +/- 1.
Then, use inverse normal

Question 15

What must be the case in reference to the mean for both the sample mean distribution and normal distribution?

Answer 15

The mean which is tested in both cases should be the same

Question 16

How do you calculate the standard deviation for a sample mean distribution, with n number of trials

Answer 16

σ² / n

Question 17

The standard deviation of a normal distribution for bananas is 3g. A random sample of 16 bananas is carried out to attain a mean mass of 60g. What is the standard deviation of the sample mean distribution?

Answer 17

(3² / 16)^1/2
= 3/4

Question 18

Which distribution must be used alongside a normal distribution when carrying out a hypothesis test?

Answer 18

Sample mean distribution

Question 19

What are the steps for carrying out a hypothesis test using a sample mean distribution?

Answer 19

• Write out the null and alternative hypothesis
• Draw out the distribution (two tail / one tail) and label significance level
• Find the standard deviation for the sample mean distribution
• Find the probability of a test statistic occuring and compare to the significance level
• Alternatively, use the inverse normal distribution to find the critical value and compare to the test statistic
• Write a conclusion either rejecting or accepting the null hypothesis