The home states of a certain group of people are distributed as follows: 53 percent are from MISSOURI, 21 percent are from KANSAS, and 26 percent are from IOWA. (No one in the group had a home state other than one of these three.)

(Note: Your answer to the question below should be rounded to three decimal places.)

Suppose we randomly select a person from this group. What is the expected value of the number of letters in the selected person's home state?

(53*8)+(21*6)+(26*4)= 654

654/100= 6.54 letters

6.64

oops I read this from my textbook where the values are a bit different.

Please ignore my misinformation world.

Well, let's do some clown math here, shall we?

If 53 percent are from MISSOURI, we can assume that every MISSOURIan takes the effort to shout out their state's name like "M-I-S-S-O-U-R-I" every time someone asks them where they're from. That's 8 letters.

If 21 percent are from KANSAS, we can assume that KANSAS natives, being more laid-back, just casually say "Kansas" without any fuss. That's 6 letters.

Lastly, if 26 percent are from IOWA, well, IOWA is a pretty friendly place, so we can just lovingly call it "Iowa" with 4 letters.

Now, let's calculate the expected value, shall we?

(53% * 8) + (21% * 6) + (26% * 4) = 4.06

So, according to my impeccable clown math, the expected value of the number of letters in the selected person's home state is approximately 4.06.

Don't worry, I didn't use any clown calculators for this one. Just good old-fashioned clown math!

To find the expected value of the number of letters in the selected person's home state, we need to calculate the average number of letters weighted by the probability of each state being selected.

Let's assign variables to represent the number of letters in each state:
M = number of letters in MISSOURI = 8
K = number of letters in KANSAS = 6
I = number of letters in IOWA = 4

We also need to calculate the probability of selecting each state:
P(M) = 53% = 0.53
P(K) = 21% = 0.21
P(I) = 26% = 0.26

Now we can calculate the expected value using the formula:

Expected value = (M * P(M)) + (K * P(K)) + (I * P(I))

Substituting the values:

Expected value = (8 * 0.53) + (6 * 0.21) + (4 * 0.26)
Expected value = 4.24 + 1.26 + 1.04
Expected value = 6.54

Therefore, the expected value of the number of letters in the selected person's home state is 6.54 (rounded to three decimal places).

5.54134