# Lesson 1What Is Normal?Develop Understanding

### 1.

Jordan scores a on his math test. The class average is with a standard deviation of . How many standard deviations below the mean did Jordan score?

### 2.

In Jordan’s science class, he scored . The class average was with a standard deviation of . How many standard deviations below the mean did Jordan score? In comparison to his peers, which test did Jordan perform better on?

### 3.

Rank the data sets below in order of greatest standard deviation to smallest:

### 4.

Robin made it to the swimming finals for her state championship meet. The times in the finals were as follows:

If Robin’s time was a , what percent of her competitors did she beat?

### 5.

Remember that in statistics, is the symbol for mean and is the symbol for standard deviation. Using technology, identify the mean and standard deviation for the data set below:

### 6.

For the data in number 5, what time would fall one standard deviation above the mean? Three standard deviations below the mean?

## Set

For each distribution, identify the properties that match with a normal distribution, and then decide if the normal curve could be used as a model for the distribution and explain why.

### 7.

1. Normal Properties:

2. Model with a normal curve? Yes or no?

### 8.

1. Normal Properties:

2. Model with a normal curve? Yes or no?

### 9.

1. Normal Properties:

2. Model with a normal curve? Yes or no?

### 10.

1. Normal Properties:

2. Model with a normal curve? Yes or no?

### 11.

1. Normal Properties:

2. Model with a normal curve? Yes or no?

### 12.

1. Normal Properties:

2. Model with a normal curve? Yes or no?

### 13.

#### a.

If two normal distributions have the same standard deviation of but different means of and , how will the two normal curves look in relation to each other?

#### b.

Draw a sketch of each normal curve.

### 14.

#### a.

If two normal distributions have the same mean of but standard deviations of and , how will they look in relation to each other?

#### b.

Draw a sketch of each normal curve below.

### 15.

The normal curve given has been labeled out to three standard deviations. Estimate what one standard deviation is for this curve.

## Go

Write the inverse of the function in the same format as it is given.

### 19.

Determine if the following functions are inverses by finding and .

and

and