Answer:
a) 0.345
b) 0.005
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 100
Standard Deviation, σ = 0.3
We are given that the distribution of lengths of lumber is a bell shaped distribution that is a normal distribution.
Formula:

a) P(length greater than 100.12 inches)
P(x > 100.12)


Calculation the value from standard normal z table, we have,

b) Standard error due to sampling:

P(length greater than 100.12 inches for the sample)
P(x > 100.12)


Calculation the value from standard normal z table, we have,

Answer:
-2/3
Step-by-step explanation:
Find a common denominator.
Multiply -1/2 by 3/3.

Combine the fractions

Reduced to lowest terms. (-4 and 6 are divisible by 2)
A function is a relation (rule) that assigns each element in the domain to exactly one element in the range.
Answer:
2nd option
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
the centre is at the midpoint of the endpoints of the diameter.
The coordinates of the centre is the average of the coordinates of the endpoints.
centre = (
,
) = (
,
) = (- 1, 3 )
the radius is the distance from the centre to either of the endpoints
using the distance formula to calculate r
r = 
with (x₁, y₁ ) = (- 1, 3 ) and (x₂, y₂ ) = (2, - 1 )
r = 
= 
= 
= 
= 
= 5
then equation of circle is
(x - (- 1) )² + (y - 3)² = 5² , that is
(x + 1)² + (y - 3)² = 25