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:
![f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0](https://tex.z-dn.net/?f=f_%7BX%7D%28x%29%3D%5Clambda%5Ccdot%20e%5E%7B-%5Clambda%20x%7D%3B%5C%20x%3E0%2C%5C%20%5Clambda%3E0)
Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:
![P(6\leq X\leq 9)=\int\limits^{9}_{6} {\lambda\cdot e^{-\lambda x}} \, dx](https://tex.z-dn.net/?f=P%286%5Cleq%20X%5Cleq%209%29%3D%5Cint%5Climits%5E%7B9%7D_%7B6%7D%20%7B%5Clambda%5Ccdot%20e%5E%7B-%5Clambda%20x%7D%7D%20%5C%2C%20dx)
![=\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:
y=.5x+-2.5
Step-by-step explanation:
This is the linear equation (y=mx+b) m means slope so your slope is .5.
4.5
pi is about 3.14 and root 23 is about 4.8 - the only number between these values is 4.5
Answer:
100*150=15000 calories
Step-by-step explanation:
100 times 150 is 15000 because you are multipling 2 people
I don't know if it is correct
just check and if it isn't then check some one elses work.
Answer:
90 is your answer
Step-by-step explanation:
first I just added all similar numbers together, then I added the answers of all the similar numbers together one-by-one, finally we find our answer, 90