Question
E RIN{ 92% 13:19 PM K Lab 5 - Sampli... a 5.3- Births: Sampling Distribution of Sample Proportion: When three births are randomly selected. the sample space for genders is bbb, bbg, bgb, bgg. gbb. gbg, ggb, and ggg. Assume that those eight outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from three births. Does the mean of the sample proportions equal the proportion of girls in three births? a) To construct the table for sampling distribution of sample proportion of girls from three births, you need to identify the sampling distribution of sample proportion of girls from three births. b) For computing the sample proportion of girls from three births, you have to find values for all possible sample proportions because each sample is equally to occur, the probability of certain proportion value is the number of occurrences of that proportion value divided by the total number osamples. c) Here I've done the first one for you Sample bbb (which would be 3 boys, 0 girls): Sample proportion of girls from three births-number of girls from three births 1-0 ProbabilityNumber of events occur1 Total number of possible outcomes d) Once your calculations are done, the table representing the sample distribution of girls from three births would be Sam in the following format: Proportion of Girls Probability 1/8 e) Any repeating values should be combined into another table in ascending order f) For the last part read the question carefully, and calculate the information requested.
Explanation / Answer
X - number of girls in 3 births
X follow binomial distribution
with n = 3 , p = 1/2
P(X =k) = 3Ck (1/2)^k * (1/2)^(3-k)
= 3Ck*(1/2)^3
= (3Ck ) / 8
1/8 = 0.125
3/8 = 0.375
event number of girl n p bbb 0 0 0.125 bbg 1 1 0.375 bgb 1 2 0.375 bgg 2 3 0.125 ggg 3 ggb 2 gbg 2 gbb 1
