Answer:
Step-by-step explanation:
we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = variable
µ = mean output
σ = standard deviation
From the information given,
µ = 14
σ = 3
1) P(x < 20)
For x = 20,
z = (20 - 14)/3 = 2
From the normal distribution table, the corresponding probability value is 0.98
% = 0.98 × 100 = 98%
2) P(11 ≤ x ≤ 17)
For x = 11,
z = (11 - 14)/3 = - 1
From the normal distribution table, the corresponding probability value is 0.16
For x = 17,
z = (17 - 14)/3 = 1
From the normal distribution table, the corresponding probability value is 0.84
P(11 ≤ x ≤ 17) = 0.84 - 0.16 = 0.68
% = 0.68 × 100 = 68%
3) P(x > 14) = 1 - P(x ≤ 14)
For x = 14,
z = (14 - 14)/3 = 0
From the normal distribution table, the corresponding probability value is 0.5
P(x > 14) = 1 - 0.5 = 0.5
% = 0.5 × 100 = 50%
4) P(5 ≤ x ≤ 17)
For x = 5,
z = (5 - 14)/3 = - 3
From the normal distribution table, the corresponding probability value is 0.00135
For x = 17,
z = (17 - 14)/3 = 1
From the normal distribution table, the corresponding probability value is 0.84
P(5 ≤ x ≤ 17) = 0.84 - 0.00135 = 0.839
% = 0.839 × 100 = 83.9%
He is incorrect because 0.9 is equal to 0.90 which is greater than 0.74 because 9 is greater than 7
Answer:
f(-10) = -19
f(2) = 4
f(-5) = -9
f(-1) = 1
f(8) = -5
Step-by-step explanation:
This is relatively simple if you understand the concept. All you have to do is take each number and then look at each inequality to see where it fits.
For example, if you take 2 and look at the first inequality, you see that 2 is not less than or equal to 5. Now if you look at the second inequality, you see that 2 is both greater than -5 and less than 5. Since 2 fits in the second inequality, you plug it into the second equation.
These functions where you have to see where the x-value fits are called piecewise functions and you will see them a lot in higher level math.
(disclaimer: I evaluated the numbers quickly, so I would doublecheck it, but I am pretty sure I didn't mess up)
I think it's C because that's the best answer.
