Respuesta :
Answer:
the probability between 9.2 and 17.6 is, 0.79237.
Step-by-step explanation:
It is given that distribution is normal.Also given the value of [tex]\mu = 12[/tex]
and [tex]\sigma = 3[/tex] .
Use : [tex]z = \frac{x-\mu}{\sigma}[/tex]
Now,
Calculate First [tex]P(X>9.2)[/tex]
then we put the value of x =9.2 in the z transform,i.e, [tex]z = \frac{x-\mu}{\sigma}[/tex]
[tex]z = \frac{9.2-12}{3}= -0.933333333[/tex]
Using the standard Normal table of N(0,1); we get
⇒ [tex]P(X>9.2) = 0.17619[/tex]
Similarly, for [tex]P(X<17.6)[/tex]
put the value of x =17.6 in the z-transform we get;
[tex]z = \frac{17.6-12}{3}=1.86666667[/tex]
By the Normal Table N(0,1); we get
⇒ [tex]P(X<17.6) = 0.96856[/tex]
Then, the probability between 9.2 and 17.6 i.e,
[tex]P(9.2<X<17.6) = 0.96856 - 0.17619=0.79237[/tex]
