Answer:
Mean is 6
Step-by-step explanation:
Mean refers to the average of the observations.
Let X be the number of different sweaters I wore during a 5-day week.
Possible values of X = 1, 2, 3, 4
For X = 1, [tex]P(X=1)=\frac{1}{5}[/tex]
For X = 2, [tex]P(X=2)=\frac{2}{5}[/tex]
For X = 3, [tex]P(X=3)=\frac{3}{5}[/tex]
For X = 4, [tex]P(X=4)=\frac{4}{5}[/tex]
To find: Mean
Solution:
[tex]\sum_{x=1}^{4}xP(X=x)=1P(X=1)+2P(X=2)+3P(X=3)+4P(X=4)\\=1\left ( \frac{1}{5} \right )+2\left ( \frac{2}{5} \right )+3\left ( \frac{3}{5} \right )+4\left ( \frac{4}{5} \right )\\=\frac{1}{5}+\frac{4}{5}+\frac{9}{5}+\frac{16}{5}\\=\frac{1+4+9+16}{5}\\=\frac{30}{5}\\=6[/tex]
