The table shows the probability of the letters in the alphabet. The information is based on randomly selecting a letter from a randomly selected passage of text. Use the information given in the table and answer the following questions.Probability with respect tothe 26 letters

A 0.04

E 0.17

I 0.065

O 0.08

U 0.03

Construct a probability distribution just for the vowelsA, E,I, O, and U.

Probability with respect to 26 letters

Probability with respect to the vowels

A

0.04 =

E

0.17=

I

0.065=

O

0.08=

U

0.03=

(B) Choose the correct bar chart which represents the probability distribution of part(a).

The accompanying data are the dailyround-trip distances to school(in miles) for 30 randomly chosen students attending a community college in a certain state. Construct astem-and-leaf display for the given data in the accompanying table. Treat the ones digit as the leaves. For anysingle-digit data, use a stem of 0.

18

33

8

13

18

24

31

17

6

12

24

16

5

24

5

23

7

15

5

24

11

19

8

17

45

22

5

13

34

8

Construct astem-and-leaf display for the given data. (Ascending order)

In a certaindistribution, the mean is 100 with a standard deviation of 2. At least what fraction of the numbers are between the following pair ofnumbers?

92 and 108 At least __of the numbers in the distribution are between 92

and 108

If your calculator finds both kinds of standarddeviation, the sample standard deviation and the population standarddeviation, which of the two will be a larger number for a given set ofdata? (Hint: Recall the difference between how the two standard deviations arecalculated.) Fill in the blank below.

The A. population standard deviation or B.sample standard deviation -will be a larger number for a given set of data.

In a distribution where the mean is 80 and the standard deviation is 3, find the largest fraction of the numbers that could meet the following requirements.

less than 68 or more than 92 Of the numbers in thedistribution, the fraction that is less than 68

or more than 92 is at most

.