Chapter 12.1, Problem 37E

Is the probability distribution in Exercise 36 theoretical or empirical? Is it different from the distribution in Exercise 35? Which one is more accurate? Explain your reasoning.

Reference:

For example, if a single letter is randomly selected from a randomly selected passage of text, the probability that it will be an E is 0.13. The probability that a randomly selected letter will be a vowel (A. E, I, O, or U) is

$(0.08+0.13+0.65+0.08+)0.03)=0.385$.

Rewrite the distribution shown in Exercise 33 as an empirical probability distribution. Give values to three decimal places. Note that the 26 probabilities in this distribution-one for each letter of the alphabet—should add up to 1 (except for. perhaps, a slight round-off error).

a. From your distribution in Exercise 34, construct an empirical probability distribution just for the vowels A, E, I, O, and U. (Hint Divide each vowel's probability, from Exercise 34, by 0.385 to obtain a distribution whose five values add up to 1.) Give values to three decimal places, b. Construct an appropriately labeled bar graph from your distribution in part (a).

Based on the occurrences of vowels in the paragraph represented by Figure 5 , construct a probability distribution for the vowels. Give probabilities to three decimal places. The frequencies are

A-31, E-34, I-20, O- 23, U -10.

Figure 5