PLS HELP!! WILL GIVE BRAINLIEST!!

Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2725hours is a

Ivan

Answer:

a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

$P(X >2) = 1-P(X\leq 2) = 1-(1- e^{-0.367 *2})=e^{-0.367 *2}= 0.48$

At most 3 hours?

$P(X \leq 3) = F(3) = 1-e^{-0.367*3}= 1-0.333 =0.667$

b) What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

$P(X > 2.725 + 2*5.540) = P(X>13.62) = 1-P(X$

What is the probability that it is less than the mean value by more than one standard deviation?

$P(X$

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}$

The cumulative distribution for this function is given by:

$F(X) = 1- e^{-\lambda x}, x\ geq 0$

We know the value for the mean on this case we have that :

$mean = \frac{1}{\lambda}$

$\lambda = \frac{1}{Mean}= \frac{1}{2.725}=0.367$

Solution to the problem

Part a

What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

$P(X >2) = 1-P(X\leq 2) = 1-(1- e^{-0.367 *2})=e^{-0.367 *2}= 0.48$

At most 3 hours?

$P(X \leq 3) = F(3) = 1-e^{-0.367*3}= 1-0.333 =0.667$

Part b

What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

The variance for the esponential distribution is given by: $Var(X) =\frac{1}{\lambda^2}$

And the deviation would be:

$Sd(X) = \frac{1}{\lambda}= \frac{1}{0.367}= 2.725$

And the mean is given by $Mean = 2.725$

Two deviations correspond to 5.540, so we want this probability:

$P(X > 2.725 + 2*5.540) = P(X>13.62) = 1-P(X$

What is the probability that it is less than the mean value by more than one standard deviation?

For this case we want this probablity:

$P(X$

8 0

3 years ago

Can someone help explain this to me?

o-na [289]

Step-by-step explanation:

A. y-5=-4x+4

y=-4x+4+5

y= -4x +9

(0,9)(9/4,0)

8 0

3 years ago

A 15-foot ladder leans against a house. The bottom of the ladder is 7 feet from the house. To the nearest degree, what angle doe

max2010maxim [7]

The ladder is forming a right triangle with the house. In this right triangle the hypotenuse is the measure of the ladder, and the distance between the house and he ladder is one of the sides of the triangle. To find the angle, $\alpha$ , that the ladder is making with the ground, we are going to use a trig function that relates the adjacent side of our angle with the hypotenuse. That trig function is Cosine.
$Cos \alpha = \frac{adjacent.side}{hypotenuse}$
$Cos \alpha = \frac{7}{15}$
$\alpha =arcCos( \frac{7}{15} )$
$\alpha =62.2$

We can conclude that the ladder make with the ground a 62° angle.

7 0

3 years ago

Triangle R Q S is cut by line segment T U. Line segment T U goes from side Q R to side Q S. The length of Q T is 32, the length

Marizza181 [45]

The statement that is true is option A that is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.

<h3>What is the line segment about?</h3>

The law of the side- splitter connote that when f the line is parallel to a side of the triangle and if that said line do intersects the other 2 sides, tt is said to divides those given sides proportionally.

So the converse means that when the sides are proportional so therefore, the side TU is said to be parallel to the side RS.

Thus;

$\frac{QT}{TR}$ = $\frac{32}{36} = \frac{8}{9}\\\\ \\$

$\\\frac{QU}{US} =\frac{40}{45} = \frac{8}{9}\\$

Therefore, the ratios are equal and as such TU is parallel to RS

Hence, The statement that is true is option A that is Line segment TU is parallel to line segment RS because StartFraction 32 Over 36 EndFraction = StartFraction 40 Over 45 EndFraction.

Learn more about Line segment from

brainly.com/question/2437195

#SPJ1

5 0

2 years ago

9/5 rename as a mixed number

Anon25 [30]

4 1/5 because 4+5=9 so 4 then you will have 1/5

3 0

2 years ago

Read 2 more answers