According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts.a. What is the mean amount spent on insurance?
b. What is the standard deviation of the amount spent?
c. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year?
d. What is the probability a family spends more than $3,000 per year?
Answers
Answer: a. 2100
b. 981.5
c. 0.471
d. 0.235
Step-by-step explanation:
Given: According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance.
If the money spent is uniformly distributed between these amounts.
Let A=$400 and B= $3,800
a. The mean amount spent on insurance =
b. The standard deviation of the amount spent=
c. To calculate, the probability they spend less than $2,000 per year on insurance per year ,it means the amount is between 400 and 2000 i.e
Amount=$2000-$400=$1600
Then P(400<insurance amount<2000)
d. Ia a family spends more than $3000 then the amount is between $3000 and $3800, i.e. Amount= $3800-$3000=$800
Now,
P(3000<insurance amount<3800)=
b. To find the standard deviation, we take the variance ((b-a)/√12) and plug in the values:
(3800 - 400)/√12
3400/√12
~981.5
c. Again, because of uniform distribution, we just have to find the percentage that all numbers less than 2000 have in the range of 400 to 3800. To make things simple, I'm going to subtract 400 from both 3800 and 2000 so the data cuts off at 0. The equation is:
1600 = 3400 * x
16/34 = x (simplified from 1600/3400)
8/17 = x
8/17 is about 0.47, or 47%, so that's your amount.
d. same thing with c, but slightly different:
3800 - 400 = 3400, 3000 - 400 = 2600
3400 - 2600 = 800
800 = 3400 * x
8/34 = x
4/17 = x
4/17 is about 0.235.
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The statement ∀x∃y(x² = y) is true for all real numbers, as for each real number x, there exists a real number y such that x² = y.
How to determine the truth value of a statement?
The statement ∀x∃y(x² = y) is true as explained below:
For every real number x, there exists a real number y such that x² = y.
For example:
If x = 2, then y = 4 because 2² = 4.
If x = -3, then y = 9 because (-3)² = 9.
Since you can always find a real number y that satisfies the equation x² = y for any real number x, the statement is true for all real numbers in its domain.
Learn more about truth value on:
#SPJ4
The statement is true. If x and y are both real numbers, the statement is:
"for every x, there exist y such that "
This is true, because you can pick any real number, square it, and obtain another real number, y. The relation is not surjective, i.e. we will not use all possible values for y, but it doesn't matter. The statement is only asking to find a value for x^2, which we can always do.