Lesson 1 What Is Normal? Develop Understanding

Ready

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:

a.

b.

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.

a square is graphed on a coordinate plane with a point at (1,0) 111000
  1. Normal Properties:

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

8.

a vertical histogram where the bars are skewed up 222444666
  1. Normal Properties:

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

9.

a box plot where the distribution is normal
  1. Normal Properties:

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

10.

a curve resembling a half of a oval is uniform on both sides of the peak MeanMedianMode
  1. Normal Properties:

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

11.

a vertical histogram where the frequency is not uniform on both sides of the peak –0.6–0.6–0.6–0.4–0.4–0.4–0.2–0.2–0.20.20.20.20.40.40.40.60.60.6000
  1. Normal Properties:

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

12.

a histogram where the x axis is labeled height and the y axis is labeled frequency in height. The distribution is mostly normal because the mean, median, and mode are at the peak. 626262646464666666686868707070727272747474Frequency of Height000222444666888Height
  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.

a bull curve with even distribution 424242434343444444454545464646474747484848494949505050515151525252535353545454555555565656

Go

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

16.

17.

18.

19.

Determine if the following functions are inverses by finding and .

20.

and

21.

and