Given:
Let the random variable x is normally distributed with mean [tex]\mu=90[/tex] and [tex]\sigma=5[/tex]
We need to determine the probability of [tex]P(X<80)[/tex]
Probability of [tex]P(X<80)[/tex]:
The formula to determine the value of [tex]P(X<80)[/tex] is given by
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Thus, we have;
[tex]P(X<80)=P(Z<\frac{80-90}{5})[/tex]
Simplifying, we get;
[tex]P(X<80)=P(Z<\frac{-10}{5})[/tex]
[tex]P(X<80)=P(Z<-2)[/tex]
Using the normal distribution table, the value of -2 is given by 0.0228
[tex]P(X<80)=0.0228[/tex]
Thus, the value of [tex]P(X<80)[/tex] is 0.0228
