Answer:
And using a calculator, excel ir the normal standard table we have that:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution for the problem
Let's say that X represent the random variable "incomes in a certain large population of college", and we know that the distribution for X is:
We select 16 teachers and we are interested on the sample mean or average, and we know that the distribution for the sample mean is given by:
And we are interested on this probability:
And we can use the z score given by:
And using a calculator, excel ir the normal standard table we have that:
277 years because 831 people/3 people per year = 277 years
Answer:
The answers are 0, 1 and −2.
Step-by-step explanation:
Let α=arctan(2tan2x) and β=arcsin(3sin2x5+4cos2x).
sinβ2tanβ21+tan2β2tanβ21+tan2β23tanxtan2β2−(9+tan2x)tanβ2+3tanx(3tanβ2−tanx)(tanβ2tanx−3)tanβ2=3sin2x5+4cos2x=3(2tanx1+tan2x)5+4(1−tan2x1+tan2x)=3tanx9+tan2x=0=0=13tanxor3tanx
Note that x=α−12β.
tanx=tan(α−12β)=tanα−tanβ21+tanαtanβ2=2tan2x−13tanx1+2tan2x(13tanx)or2tan2x−3tanx1+2tan2x(3tanx)=tanx(6tanx−1)3+2tan3xor2tan3x−3tanx(1+6tanx)
So we have tanx=0, tan3x−3tanx+2=0 or 4tan3x+tan2x+3=0.
Solving, we have tanx=0, 1, −1 or −2.
Note that −1 should be rejected.
tanx=−1 is corresponding to tanβ2=3tanx. So tanβ2=−3, which is impossible as β∈[−π2,π2].
The answers are 0, 1 and −2.
Add the percentage as a decimal
To 1 to get 1.20
Multiply:
340 x 1.20 = 408
Answer: 408