lucy makes a probability distribution where the random variable x represents the total number of days her…

lucy makes a probability distribution where the random variable x represents the total number of days her weather app says it is expected to rain next week. then she calculates the mean of the probability distribution.\nis lucys calculation for the mean of the probability distribution correct? use the drop - down menus to explain.\n\n|x|p(x)|\n|----|----|\n|1|0.5|\n|2|0.25|\n|3|0.15|\n|4|0.1|\n|5|0|\n\nmean of the probability distribution = 1(0.5)+2(0.25)+3(0.15)+4(0.1)=1.85\n\nclick the arrows to choose an answer from each menu.\nthe mean of the probability distribution is calculated by choose... . the mean of the probability distribution is choose... . lucy is choose... .

lucy makes a probability distribution where the random variable x represents the total number of days her weather app says it is expected to rain next week. then she calculates the mean of the probability distribution.\nis lucys calculation for the mean of the probability distribution correct? use the drop - down menus to explain.\n\n|x|p(x)|\n|----|----|\n|1|0.5|\n|2|0.25|\n|3|0.15|\n|4|0.1|\n|5|0|\n\nmean of the probability distribution = 1(0.5)+2(0.25)+3(0.15)+4(0.1)=1.85\n\nclick the arrows to choose an answer from each menu.\nthe mean of the probability distribution is calculated by choose... . the mean of the probability distribution is choose... . lucy is choose... .

Answer

Explanation:

Step1: Recall mean formula for probability distribution

The formula for the mean $\mu$ of a discrete - probability distribution is $\mu=\sum_{i}x_{i}P(x_{i})$, where $x_{i}$ are the values of the random variable and $P(x_{i})$ are their corresponding probabilities.

Step2: Check Lucy's calculation

Lucy used the formula $\mu = 1(0.5)+2(0.25)+3(0.15)+4(0.1)$. She correctly multiplied each value of $X$ by its corresponding probability $P(X)$ and summed them up.

Answer:

The mean of the probability distribution is calculated by multiplying each value of the random variable $X$ by its corresponding probability $P(X)$ and then summing these products. The mean of the probability distribution is $1.85$. Lucy is correct.