in-a-biology-study-a-population-consists-of-three-blue-butterflies-and-two-orang

Question

In a biology study, a population consists of three blue butterflies and two orange butterflies. Two butterflies are randomly chosen with replacement. What is the sampling distribution of the proportion of blue butterflies in the samples?

Accepted Answer

Sample Proportion (p^)Probability (P)19251212250425\begin{array}{c|c}	ext{Sample Proportion }\left(\hat{p}ight) & 	ext{Probability }\left(Pight)\ 1 & \frac{9}{25}\ \frac12 & \frac{12}{25}\ 0 & \frac{4}{25}\end{array}

Answer

Sample Proportion (p^)Probability (P)14251217250425\begin{array}{c|c}	ext{Sample Proportion }\left(\hat{p}ight) & 	ext{Probability }\left(Pight)\ 1 & \frac{4}{25}\ \frac12 & \frac{17}{25}\ 0 & \frac{4}{25}\end{array}

Answer

Sample Proportion (p^)Probability (P)19251242501225\begin{array}{c|c}	ext{Sample Proportion }\left(\hat{p}ight) & 	ext{Probability }\left(Pight)\ 1 & \frac{9}{25}\ \frac12 & \frac{4}{25}\ 0 & \frac{12}{25}\end{array}

Answer

Sample Proportion (p^)Probability (P)19251210250625\begin{array}{c|c}	ext{Sample Proportion }\left(\hat{p}ight) & 	ext{Probability }\left(Pight)\ 1 & \frac{9}{25}\ \frac12 & \frac{10}{25}\ 0 & \frac{6}{25}\end{array}