Answer:
Mean = 3.7
Variance = 2.61
Step-by-step explanation:
From the data given; we can represent our table into table format for easier solution and better understanding.
Given that:
A highway engineer knows that his crew can lay 5 miles of highway on a clear day, 2 miles on a rainy day, and only 1 mile on a snowy day
Let X represent the crew;
P(X) represent their respective probabilities
clear day rainy day snowy day
X 5 2 1
P(X) 0.6 0.3 0.1
From Above; we can determine our X*P(X) and X²P(X)
Let have the two additional columns to table ; we have
X P(X) X*P(X) X²P(X)
5 0.6 3 15
2 0.3 0.6 1.2
1 0.1 0.1 0.1
Total 1.0 3.7 16.3
The mean can be calculated by using the formula:
Therefore ; mean = 3.7
Variance
Variance = 16.3 -3.7²
Variance = 16.3 - 13.69
Variance = 2.61