Mathematics, 20.03.2020 02:00, Jasoncookies23

Let X represent the amount of time until the next student will arrive in the library parking lot at the university. The distribution of arrival time can be modeled using an exponential distribution with rate 1/4 arrivals per minute. Find the probability that it will take more than 10 minutes for the next student to arrive at the library parking lot. Group of answer choices 0.082085 0.329680 0.917915 0.670320

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Probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is 0.082085.

Step-by-step explanation:

We are given that the distribution of arrival time can be modeled using an exponential distribution with rate 1/4 arrivals per minute.

Let X = Amount of time until the next student will arrive in the library parking lot at the university.

The probability distribution for exponential distribution is given by;

$f(x) = \lambda e^{-\lambda x} ; x 0$

where, $\lambda$ = parameter of this distribution or the arrival rate = $\frac{1}{4}$ = 0.25

So, X ~ Exp( $\lambda = 0.25$ )

Now, to find the less than or greater than probabilities in exponential distribution we use the Cumulative distribution function of exponential function, i.e.;

$F(x) = P(X \leq x) = 1 - e^{-\lambda x} ; x 0$

So, probability that it will take more than 10 minutes for the next student to arrive at the library parking lot is given by = P(X > 10 minutes)

P(X > 10) = 1 - P(X $\leq$ 10)

= 1 - [ $1 - e^{-0.25 \times 10}$ ]

= $e^{-2.5}$ = 0.082085

Therefore, probability that it will take more than 10 minutes for the next student to arrive is 0.082085.

answered: Guest

step-by-step explanation:

answered: Guest

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.