Respuesta :
Answer:
a. 19
Step-by-step explanation:
We have a normal distribution with parameters [tex]\mu=69.0[/tex] and [tex]\sigma=2.8[/tex].
If the limits that requires the U.S Maine Corps is a height between 64 and 78 inches, we can express the proportion of rejected as:
[tex]P(rejected)=P(x<64.0)+P(x>78.0)[/tex]
We can calculate the z-values to calculate this probabilities by table.
[tex]z_1=\frac{x_1-\mu}{\sigma}=\frac{64.0-69.0}{2.8}= -1.786\\\\z_2=\frac{x_2-\mu}{\sigma}=\frac{78.0-69.0}{2.8}=3.214[/tex]
Then we can express the probability as
[tex]P(rejected)=P(z<-1.786)+P(z>3.214)[/tex]
[tex]P(rejected)=0.03705+0.00065=0.0377[/tex]
If there are 500 men to enlist, the expected amount to be rejected is
[tex]M=500*0.0377=18.85 \approx 19[/tex]
