Answer:
a) 0.0062
b) 0.4938
Step-by-step explanation:
a)
We need to convert each to z score and use z-table to find the probabilities.
The formula for z score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where [tex]\mu[/tex] is the mean (given as 12), and
[tex]\sigma[/tex] is the standard deviation (given as 2)
So we have:
[tex]P(x<7)=P(z<\frac{7-12}{2})=P(z<-2.5)=0.0062[/tex]
Hence, probability is 0.0062
b)
Here, we want between 7 and 12, we already found z-score of x = 7 to be -2.5. Let's find z score of x = 12 using the formula:
[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{12-12}{2}\\z=0[/tex]
So we have:
[tex]P(7<x<12)=P(-2.5<z<0) =0.4938[/tex]
Hence, probability is 0.4938
