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 = \(\frac{A+B}{2}=\frac{3800+400}{2}=\frac{4200}{2}=\$2100\)
b. The standard deviation of the amount spent=
\(\sqrt{\frac{(B-A)^2}{12}}\\=\sqrt{\frac{(3800-400)^2}{12}}\\=\sqrt{\frac{(3400)^2}{12}}\)
\(=\frac{3400}{\sqrt{12}}=981.495\approx981.5\)
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)\(=\frac{amount}{B-A}=\frac{1600}{3400}=0.4705\approx0.471\)
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)=\(\frac{800}{3400}=\frac{4}{17}=0.235\)
