Answer: 96.2%
Step-by-step explanation:
Assume that the heights of American men are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = heights of American men.
µ = mean height
σ = standard deviation
From the information given,
µ = 69.0 inches
σ = 2.8 inches
the probability of men that have heights between 64 and 78 inches is expressed as
P(64 ≤ x ≤ 78)
For x = 64,
z = (64 - 69)/2.8 = - 1.79
Looking at the normal distribution table, the probability corresponding to the z score is 0.037
For x = 78,
z = (78 - 69)/2.8 = 3.2
Looking at the normal distribution table, the probability corresponding to the z score is 0.999
Therefore,
P(64 ≤ x ≤ 78) = 0.999 - 0.037 = 0.962
Therefore, the percent of men meeting these height requirements is
0.962 × 100 = 96.2%
Looking at this problem in terms of geometry makes it easier than trying to think of it algebraically.
If you want the largest possible x+y, it's equivalent to finding a rectangle with width x and length y that has the largest perimeter.
If you want the smallest possible x+y, it's equivalent to finding the rectangle with the smallest perimeter.
However, the area x*y must be constant and = 100.
We know that a square has the smallest perimeter to area ratio. This means that the smallest perimeter rectangle with area 100 is a square with side length 10. For this square, x+y = 20.
We also know that the further the rectangle stretches, the larger its perimeter to area ratio becomes. This means that a rectangle with side lengths 100 and 1 with an area of 100 has the largest perimeter. For this rectangle, x+y = 101.
So, the difference between the max and min values of x+y = 101 - 20 = 81.
Answer:a. μ = 9.667 hours
b. σ = 1.972 hours
c. SE = 0.805 hour
Sample size (n) = 6
Sample data (xi) = 10, 8, 9, 7, 11, 13
a. Mean time spent in a week for this course by students:
Sample mean is given by:
Mean time spent in a week per student is 9.667 hours
b. Standard deviation of the time spent in a week for this course by students:
Standard deviation is given by:
c. Standard error of the estimated mean time spent in a week for this course by students:
Standard error is given by:
To solve the given system of equations for substitution you:
1. Solve in one of the equations a variable.
For the given options the one that is correct is solve the first equation for y, by adding x to both sides:
