Doing this assignment and was wondering if i got the right answers
According to the Census Bureau publication Current Population Reports, the probability distribution for household size (number of people per household, say X) in the United States is as follows. For the purpose of the next two questions, the experiment consists of randomly selecting a household in the United States and observing the number of people living there.
x 1 2 3 4 5 6 7
P(X = x) 0.16 0.32 0.05 0.31 0.10 0.05 0.01
How many people can we expect to see living in the randomly chosen household?
Answer
4.14
3.06
4.00
1.79
1.24
What is the probability that the randomly selected household will contain more than 4 people?
Answer
0.47
0.31
0.16
0.84
0.53
For the first one i got 1.79 and for the second i don't know if i did it right but i got .53
The expectation value, or mean value, is the sum of the x*P(x) products, which is 3.06
Of course, one would not expect to find 6% of a person in a house. On the other hand, 3 is a relatively unlikely number for this distribution. 2 and 4 are seen much more often.
I do not like the way the question is worded. If they want the mean vaue, they should say so.
For the second, you do not need to use a normal distribution and compute the standard deviation etc.. Just add P(5), P(6) and P(7). You get 0.16
Thanks drwls
To find the expected number of people in the randomly chosen household (first question), you need to multiply each value of x by its corresponding probability and then sum them up. Let's perform the calculations:
x: 1 2 3 4 5 6 7
P(X = x): 0.16 0.32 0.05 0.31 0.10 0.05 0.01
Expected value (E):
E = (1 * 0.16) + (2 * 0.32) + (3 * 0.05) + (4 * 0.31) + (5 * 0.10) + (6 * 0.05) + (7 * 0.01)
E = 0.16 + 0.64 + 0.15 + 1.24 + 0.50 + 0.30 + 0.07
E ≈ 4.14
So the correct answer for the first question is 4.14.
For the second question, we need to find the probability that the number of people in the household is more than 4. To do this, we sum up the probabilities for x values greater than 4:
P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7)
P(X > 4) = 0.10 + 0.05 + 0.01
P(X > 4) = 0.16
Therefore, the correct answer for the second question is 0.16. Your answer of 0.53 is incorrect.
I hope this helps! Let me know if you have any further questions.