Americans spend an average of 2 hours per day online. If the standard deviation is 23 minutes, find the range in which at least 75% of the data will lie.

75% of the data lies on the interval [1.5592, 2.4408]

Step-by-step explanation:

Let X be the amount of hours a random american spends online per day. X has normal distribution with parameters μ = 2 and σ = 23/60 = 0.383 . The standarization of X, W is

Which has distribution N(0,1). The values of the cummulative distribution function of W are tabulated and they can be found in the attached file.

We will find and interval centered in the mean 2 in which the probability that a random american belongns to that interval is 0.75. The interval has the form

I = [2-Z , 2+Z]

As a consecuence

Since W is symmetric respect to 0, then

Thus, the last expression is equal to . We conclude that

Looking at the table, we will find that Z/0.383 = 1.15, then Z = 1.15*0.383 = 0.4408. Therefore, the interval we are looking for is [2-0.4408, 2+0.4408] = [1.5592, 2.4408].

1.3

step-by-step explanation:

3x2=6   9x+6

bring down the 6 on both sides

6+6=12

12= 9x

divide by 9

12/9 =

1.3 =x

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240