Question

the brazilian samba is an upbeat, rhythmic dance performed at celebrations and festivals. jordon is taking brazilian samba dance lessons from a friend. the probability distribution table shows the experimental probability that jordons dance lessons will be a given amount of time. what is the mean length of time, in minutes, of the dance lessons?

minutes, $x$	probability, $p(x)$
30	0.6
35	0
40	0.2
55	0.1

brazilian samba dance lessons
type the number in the box.
minutes

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 possible values and $P(x_{i})$ are their corresponding probabilities.

Step2: Calculate the product for each pair

For $x = 25$ and $P(25)=0.1$, the product is $25\times0.1 = 2.5$.
For $x = 30$ and $P(30)=0.6$, the product is $30\times0.6=18$.
For $x = 35$ and $P(35)=0$, the product is $35\times0 = 0$.
For $x = 40$ and $P(40)=0.2$, the product is $40\times0.2 = 8$.
For $x = 55$ and $P(55)=0.1$, the product is $55\times0.1=5.5$.

Step3: Sum up the products

$\mu=2.5 + 18+0 + 8+5.5=34$.

Answer:

34