Suppose a normal distribution has a mean of 79 and a standard deviation of 7. What is
A. 0.16 B. 0.025 C. 0.84 D. 0.975​

P(X ≤ 65) = P((X - 79)/7 ≤ (65 - 79)/7) = P(Z ≤ -2)

where Z follows the standard normal distribution with mean 0 and standard deviation 1.

Recall that for any normal distribution with mean µ and s.d. σ, we have

P(|X - µ| ≤ 2σ) ≈ 0.95

which in the case of Z translates to

P(-2 ≤ Z ≤ 2) ≈ 0.95

Now,

P(-2 ≤ Z) + P(-2 ≤ Z ≤ 2) + P(Z ≥ 2) = 1

==>   P(-2 ≤ Z) + P(Z ≥ 2) ≈ 0.05

Any normal distribution is symmetric about its mean, so P(-2 ≤ Z) = P(Z ≥ 2), and this gives us

==>   2 P(-2 ≤ Z) ≈ 0.05

==>   P(-2 ≤ Z) ≈ 0.025

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180