APEX AP Stats 2.2.1 Raw and Standardized Scores Study Guide.

What does the empirical rule cover?

only 3 standard deviations of the mean in either direction

Z-Score (standardized scores)

tells how many standard deviations a x-value is away from the mean

Z-score formula

z = (x - μ)/σ z=(x-mean)/standard deviation

How are the values of z typically expressed/rounded to?

the hundredth place

What do z-scores allow you to do?

convert your x-values to a universal standard, then find the proportion/percentage between any 2 x-values. 1. Allow you to standardize an x-value 2. Can be negative 3. Areas are always positive

What are the mean, median, and mode equal to in a standard normal distribution?

0

What is the normal distribution's curve area equal to?

1

How do you read a normal curve table?

1. First column heading = first two digits of a standardized z-score 2. First row heading = last digit of a standardized z-score 3. Each cell = areas/the proportion of observations below the z-score

How do you convert an x-value into a z-score?

x= zσ + μ

How do you find the percent of something lying between two z-scores?

1. Find the cell for each z-score 2. Find the area for each z-score 3. Subtract the larger area by the smaller one 4. The difference is the percent difference between both z-scores

How do you find the population proportion for the interval between two z-scores?

1. Find the area of both z-scores 2. Subtract the larger area by the smaller area 3. The difference is the population proportion between the two z-scores

What things can be derived from the area of the normal curve?

1. 68% of the area under the normal curve falls in 1 standard deviation of the mean in either direction 2. 68% of the population lies within one standard deviation of the mean in either direction 3. There's a 68% probability that a person from the population's score falls in one standard deviation of the mean

How do you convert x-values into a population proportion?

1. Convert x-scores into z-scores 2. Translate z-scores into areas/population proportions 3. Subtract the two areas

How do you convert a percentile into an x-value?

1. Find the percentile as an area in the normal curve table 2. Translate the area into a z-score 3. Translate the z-score into an x-value