Question

hannah has a chicken coop with 6 hens. let x represent the total number of eggs the hens lay on a randomly chosen day. the distribution for x is given in the table. what is the mean of the distribution? 3 3.5 4 4.2

Explanation:

Step1: Recall the formula for the mean of a discrete probability distribution

The mean $\mu$ of a discrete probability distribution is given by $\mu=\sum_{i}x_{i}p_{i}$, where $x_{i}$ are the values of the random variable and $p_{i}$ are their corresponding probabilities.

Step2: Calculate each term $x_{i}p_{i}$

• For $x = 0$ and $p=0.02$: $0\times0.02 = 0$
• For $x = 1$ and $p = 0.03$: $1\times0.03=0.03$
• For $x = 2$ and $p = 0.07$: $2\times0.07 = 0.14$
• For $x = 3$ and $p = 0.12$: $3\times0.12=0.36$
• For $x = 4$ and $p = 0.30$: $4\times0.30 = 1.2$
• For $x = 5$ and $p = 0.26$: $5\times0.26=1.3$
• For $x = 6$ and $p = 0.18$: $6\times0.18 = 1.08$

Step3: Sum up all the terms

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Answer:

4.2