Answer:
The probability that in a randomly selected game, the player scored between 12 and 20 points is 95%.
Step-by-step explanation:
Given information: The population mean is 16 and standard deviation is 2.
We need to find the probability that in a randomly selected game, the player scored between 12 and 20 points.
[tex]P(12<x<20)[/tex]
[tex]12=16-2(2)=\mu-2\sigma[/tex]
[tex]20=16+2(2)=\mu+2\sigma[/tex]
So, we need to find the value of
[tex]P(\mu-2\sigma<x<\mu+2\sigma)[/tex]
According to the empirical rule:
[tex]P(\mu-\sigma<x<\mu+\sigma)=68\%[/tex]
[tex]P(\mu-2\sigma<x<\mu+2\sigma)=95\%[/tex]
[tex]P(\mu-3\sigma<x<\mu+3\sigma)=99.7\%[/tex]
Using the empirical rule, we get
[tex]P(\mu-2\sigma<x<\mu+2\sigma)=95\%[/tex]
[tex]P(12<x<20)=95\%[/tex]
Therefore the probability that in a randomly selected game, the player scored between 12 and 20 points is 95%.
