Question

A sample of four chocolate bars are randomly selected from a box of ten. Six of the chocolates in the box are milk chocolate. a. Create a probability distribution table showing the sampling distribution of the sample proportion of milk chocolate bars in the sampl

Answer 1

Explanation:

There are 10 chocolate bars in the box, 6 of them are milk chocolate bars. So the probability of chosing milk chocolate bar is
`p=(6)/(10)=0.6` and the probability of chosing not milk chocolate bar is
`q=(10-6)/(10)=0.4.`

Chosing 4 chocolate bars, you can choose 0, 1, 2, 3, 4 milk chocolate bars. Find probabilities:

`P(\text{Number of milk chocolate bars}=0)=C^(4)_0p^0q^4=1\cdot 0.6^0\cdot 0.4^4=0.4^4=0.0256`

`P(\text{Number of milk chocolate bars}=1)=C^(4)_1p^1q^3=4\cdot 0.6^1\cdot 0.4^3=4\cdot 0.6\cdot 0.064=0.1536`

`P(\text{Number of milk chocolate bars}=2)=C^(4)_2p^2q^2=6\cdot 0.6^2\cdot 0.4^2=6\cdot 0.36\cdot 0.16=0.3456`

`P(\text{Number of milk chocolate bars}=3)=C^(4)_3p^3q^1=4\cdot 0.6^3\cdot 0.4^1=4\cdot 0.216\cdot 0.4=0.3456`

`P(\text{Number of milk chocolate bars}=4)=C^(4)_4p^4q^0=1\cdot 0.6^4\cdot 0.4^0=1\cdot 0.1296\cdot 1=0.1296`

So, a probability distribution table is