Chapter 3 stats yr 2

Question 1

What is the difference between the normal distribution and the binomial distribution?

Answer 1

Normal distribution is continuous, while the binomial distribution is discrete

Question 2

Give examples of variables that follow the normal distribution and are therefore continuous.

Answer 2

IQ scores, height and weight

Question 3

What are the characteristics of the normal distribution?

Answer 3

• it is symmetrical (mean = median = mode)
• has a bell-shaped curved with asymptotes at each end

Question 4

Answer 4

μ represents the mean and
σ represents the standard deviation.

Question 5

What is the total area under the normal distribution curve?

Answer 5

1

Question 6

What is the 68-95-99.7 rule?

Answer 6

• 68% of data is within one standard deviation of the mean
• 95% of data is within two standard deviations of the mean
• 99.7% of data is within three standard deviations of the mean

Question 7

When using the ‘Normal CD’ function on your calculator, what do you enter as the upper bound, if not given?

Answer 7

A very large value e.g. 100,000

Question 8

When using the ‘Normal CD’ function on your calculator, what do you enter as the lower bound, if not given?

Answer 8

A very small value e.g. -100,000

Question 9

Why is this true?

Answer 9

• As individual exact values have a probability of 0, because it is so infinitely specific that it doesn’t register as a probability mass

Question 10

Why does ≤ and < give the same result?

Answer 10

Question 11

Answer 11

Question 12

Answer 12

Question 13

Answer 13

Question 14

Why do we standardise our data (using coding)?

Answer 14

Because the data is much easier to analyse and work with

Question 15

How is the standard normal distribution denoted?

Answer 15

Question 16

What is the formula for converting your variable into a standard normal variable?

Answer 16

Question 17

What is this notation equivalent to?

Answer 17