Chapter 5

Question 1

Density function

Answer 1

ANy f(x) function that can be used for the probability distribution of a continuous random variable

Question 2

Density function conditions

Answer 2

1. For all numbers f(x)greater or equal to 0, the graph never drops below the x axis
2. The area under the region f(x) is 1

Question 3

Normal distribution

Answer 3

The probability distribution corresponding with a density function for a bell curve with mean and standard deviation parameters

Question 4

Normal random variable

Answer 4

A continuous random variable that is described by the parameter of normal distribution

Question 5

Relationship with SD and probability

Answer 5

Inverse relationship (SD increases probability decreases etc.)

Question 6

Standard normal distribution

Answer 6

A normally distributed random variable with mean of 0 ad SD of 1

Question 7

Left area

Answer 7

P(Z<z-score)

Question 8

Right area

Answer 8

1. 1-Left area
2. P(Z<-z)

Question 9

Area between
P(z_1<Z<z_2)

Answer 9

P(Z<z_2)-P(Z<z_1)

Question 10

Finding a standard normal variable for a given area

Question 11

Probability for general normal random variables

Answer 11

P(a<x<b)=P(zscore of a<Z<zscore of b)

-Z denoted a standard normal random variable
-a can be any number from -inf and above
-b can be any number from inf and below

Question 12

Tail distribution

Answer 12

A certain max or minimum (x*) is stated by the question and you need to find the probability of that happening

To do this you need to find z* which is just the z-score of x* and then answering the question by finding what value you are trying to find (x* or the value that is min/max for x* to be true)