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Masteriza [31]
3 years ago
5

The quotient of two and five times a number

Mathematics
1 answer:
trasher [3.6K]3 years ago
8 0
Answer: 2 / 5x
Explanation:
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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
Help???????????!!!!!!!!!!!
Butoxors [25]
Salutations!

12 \frac{2}{3}

- 9 \frac{3}{4}

= \frac{38}{3} 

Then,

- 9 \frac{3}{4}

- \frac{39}{4}

Next, our final answer:

= \frac{35}{12}

= 2 \frac{11}{12} 

Our decimal would be 2.916667

Hopefully This Helps!!!

 
3 0
3 years ago
What do you call an event where it doesn’t effect the other?<br> A. Dependent<br> B. Independent
devlian [24]
Independent. No need to thank me.
6 0
3 years ago
Read 2 more answers
N f(x) = 2x , x=5. What is the value of the function?
wel
Plug the 5 into the x in the equation 2x. it should be 2(5) which equals 10.
6 0
3 years ago
To save money, you put $200 in your bank account each week. after saving for 44 weeks, you have $1,700 dollars in your account.
Evgesh-ka [11]
Y-1700 = 200(x-4) ..............
7 0
3 years ago
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