Question

bill estimates that 20 people will attend the seminar if it does not rain and 12 people will attend if it rains. the weather forecast indicates a 40% chance it will not rain and a 60% chance it will rain on the day of the seminar. determine the expected number of people who will attend the seminar.
question 3
a 12.8
b 14.6
c 15.2
d 18.7
5 points
19 of 20 questions remaining

Explanation:

Step1: <Calculate the expected number for no - rain>

The number of people if no - rain is \(20\), and the probability of no - rain is \(P(\text{no - rain})=0.4\). The contribution to the expected value is \(20\times0.4\).

$$20\times0.4 = 8$$

Step2: <Calculate the expected number for rain>

The number of people if rain is \(12\), and the probability of rain is \(P(\text{rain}) = 0.6\). The contribution to the expected value is \(12\times0.6\).

$$12\times0.6=7.2$$

Step3: <Sum the two contributions>

The expected number of people \(E(X)\) is the sum of the two contributions from Step 1 and Step 2.

$$E(X)=20\times0.4 + 12\times0.6=8 + 7.2$$

Answer:

\(15.2\) (Option C)