For this discussion board assignment, use the applet to simulate results for 100

Question

For this discussion board assignment, use the applet to simulate results for 100 couples, where each couple is planning on having 5 children, and the constant probability of having a boy is 0.40.

Create Thread and answer the following questions.

Based on your simulation, how many couples had 0 boys, 1 boy, 2 boys, 3 boys, 4 boys, and a destroyed house (5 boys)?

Use your results to calcuate the mean number of boys out of the 100 couples.

Now use the formula for theoretical binomial probability (see #2) to find the probability of exactly x = 1, 2, 3, and 4 boys and compare these to the results of your simulation.

Outcomes: (out of 100)

# of Boys . Total

0 . 7

1 . 19

2 . 36

3 . 26

4 . 11

5 . 1

Explanation / Answer

Based on simulation, the number of couples with 0 boy is 6, 1 boy is 23, 2 boys is 39, 3 boys is 26, 4 boys is 6, 5 boys is 0.

Using P(X,r)=nCr(p)^r(1-p)^n-r, where, p is th eprobability of success, n is the number of trials, and r is the specific number of success in n trials.

P(X=5)=5C5(0.40)^5(1-0.40)^0=0.01024

According to simulation, out of 100 couples, 0 couples has 5 boys, which means, P(X=5)=0/100=0, which is in accordance with very negligle probability computed theoretically.

Mean number of boys, mu=np=5*0.40=2

P(X=1)=5C1(0.40)^1(1-0.40)^4=0.2592; P(X=2)=0.3456, P(X=3)=0.2304, P(X=4)=0.0768

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