YR 2 topic 3 (statistics)

Question 1

continuous random variables

area of curves

Answer 1

area under the curve represents probabilities

total area under curve = 1

Question 2

normal distribution

Answer 2

use µ & σ

point of inflection on normal curve = µ +- σ

Question 3

mean

Answer 3

x bar = sample mean

µ = population mean

Question 4

standard deviation

Answer 4

s = sample standard deviation
σ = population standard deviation

Question 5

normally distributed variable

Answer 5

1. 68% of data lies within 1 standard deviation of mean
2. 1 deviation from the mean the curve has points of inflexion
3. 95% of data lies within 2 standard deviations of the mean
4. 99.7% of data lies within 3 standard deviations of the mean
5. values more than 5 standard deviations from mean have probability close to 0

Question 6

inverse normal

Answer 6

using the area

Question 7

standard normal distribution

Answer 7

z~ N (0, 1 squared)

mean = 0
standard deviation = 1

Z = X - µ divided by σ