Math

StatisticsQ&A Library3. Predicting when a Florida hurricane occurs (Southeastern Geographer (Summer 2009))In an effort to minimize the monetary losses that result from a devastating Florida hurricane, partof the researchers' analysis included a graphic showing the sequence number of tropical stormswithin a season that are most likely to develop into a hurricane. Data for 67 hurricanes aresummarized in the table. Let x represent the sequence number of a Florida tropical storm withina season that develops into a hurricaneenceNumber1012131415a) Explain why x represents a discrete random variableb) Specify the probability distribution for xc) Find P(x-5)d) Find P(x < 5)e) Find E(x) and interpret the resultf) Is it likely to observe a hurricane after the 15th tropical storm of the season? ExplainQuestion

Asked Feb 14, 2019

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Part d, e, f

Step 1

**The probability distribution for the variable x:**

*Conditions of the discrete probability distribution:*

- The probabilities of all the values of the variable
*X*must lie between 0 and 1. - The sum of probabilities of all the values of
*X*must be equal to “1”.

The total number of developed hurricanes is *n *= 67.

The general formula to obtain the probability of an event is,

Probability of an event *= *(Number of favourable cases for the event)/(Total number of cases).

Here, the probabilities for the values of the variable *x *is obtained as,

Probability of *x _{i}* = (Number of hurricanes developed for that particular

The probability distribution table of the variable *x* is given below:

Step 2

**d.**

**Find the value of P(x < 5).**

Here, the sequence number of tropical storms within a season is less than 5. That is, the variable *x *takes the values 1, 2, 3 and 4.

From the above obtained probability distribution of the variable *x*, the value of *P*(*x *= 1) is 0.0597, the value of *P*(*x *= 2) is 0.1493, the value of *P*(*x *= 3) is 0.0746, the value of *P*(*x *= 4) is 0.0896.

The value of *P*(*x *< 5) is obtained as **0.3732** from the calculation given below:

Step 3

**e.**

**Find the mean of the variable x.**

The general formula to obtain the expected value of a discrete random variable is,

*E*(*X*) = ∑*X*P*(*X*)

The values of *x * and *P*(*x*) taken from the probability distribution table ob...

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