Normal Distribution

Question 1

What is standard deviation?

Answer 1

A measure of how spread the values of a continuous variable are from the mean.

Question 2

What is variance?

Answer 2

The average of the square differences from the mean.

Question 3

Why is probability important?

Answer 3

• allows us to determine how representative our sample is of the wider population
• allows us to say how likely we would get the same results from another sample
• allows us to make inferences about the population even when we don’t know the true population parameters

Question 4

List the 7 features of a normal distribution.

Answer 4

• Normal distributions are symmetrical around their mean.
• Mean = median = mode
• Area under the normal curve = 1
• Normal distributions are denser in the centre and less dense in the tails
• Defined by two parameters, the mean and the standard deviation
• 68% of the area of the normal distribution is within one standard deviation of the mean
• 95% of the area of the normal distribution is within two standard deviations of the mean

Question 5

What does a smaller value of standard deviation mean?

Answer 5

Indicates that on average, observations do not deviate far from the mean.

Question 6

What are the two properties of a standard normal distribution?

Answer 6

Mean = 0, standard deviation = 1.

Question 7

What is the purpose of Z-scores?

Answer 7

Used to transform any value from any normal distribution into its corresponding value on a standard normal distribution.

Question 8

What is the formula for Z?

Answer 8

Z = (X - mean) / standard deviation. X = observation

Question 9

What is the Z-score?

Answer 9

The number of standard deviation units from the mean.

Question 10

How are Z-scores spread around the mean?

Answer 10

• Positive values fall above the mean
• Negative values fall below the mean

Question 11

What is the Central Limit Theorem?

Answer 11

For random sample, the larger the sample size (n), the closer the sampling distribution of the sample mean (x) is approximate to the normal curve.

Question 12

What is standard error?

Answer 12

The standard deviation of the sampling distribution of the true mean.

Question 13

What does the standard error tell us?

Answer 13

How much our sample is likely to differ randomly from the population, even when we don’t know the mean of the population.

Question 14

What is standard error affected by?

Answer 14

The variation in our data and the sample size.

Question 15

What is the formula for standard error?

Answer 15

standard deviation / (square root of sample size)

Question 16

What is the formula of a standard error of a proportion?

Answer 16

S(p) = square root of p(1-p) / N . p = proportion