Answer:
The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.
Step-by-step explanation:
Let the random variable <em>X</em> represent the time a child spends waiting at for the bus as a school bus stop.
The random variable <em>X</em> is exponentially distributed with mean 7 minutes.
Then the parameter of the distribution is,
.
The probability density function of <em>X</em> is:
Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:
![=\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148](https://tex.z-dn.net/?f=%3D%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7B%5Cfrac%7B1%7D%7B7%7D%5Ccdot%20e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B7%7D%5Ccdot%20%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7Be%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%7D%20%5C%2C%20dx%20%5C%5C%5C%5C%3D%5B-e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%20x%7D%5D%5E%7B9%7D_%7B6%7D%5C%5C%5C%5C%3De%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%206%7D-e%5E%7B-%5Cfrac%7B1%7D%7B7%7D%20%5Ccdot%209%7D%5C%5C%5C%5C%3D0.424373-0.276453%5C%5C%5C%5C%3D0.14792%5C%5C%5C%5C%5Capprox%200.148)
Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.
Answer:
1,500,000,000
Step-by-step explanation:
(5/4)•(4/3)•(3/5)
So you multiply all of them basically
The amount more annually a $115,000 10-year term insurance at age 35 cost Bernard than someone of the same age without health issues is $24.
<h3>What are insurance premiums?</h3>
The insurance premium is paid as a cost to cover a possible loss that is unseen.
The annual premium rate as a percentage of the value insured a person at age 35 has to pay is 0.14%.
From the given information, we have that the amount a 35-year-old without health issues will pay per $1,000 is $1.40
The amount to be paid for $115,000 is 115 × $1.4 = $161
The amount Bernard pays = 15% more
= 1.15 × $161
= $185.15
Therefore,
The amount more Bernard has to pay = $185.15 - $161
= $24.15 ≈ $24
Learn more about insurance premiums here:
brainly.com/question/3053945
Multipy 3 by 6 multiply 1 by 4 and 7 by 4 then add the numbers
