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3. 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? Explain

Question
3. 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, part
of the researchers' analysis included a graphic showing the sequence number of tropical storms
within a season that are most likely to develop into a hurricane. Data for 67 hurricanes are
summarized in the table. Let x represent the sequence number of a Florida tropical storm within
a season that develops into a hurricane
ence
Number
10
12
13
14
15
a) Explain why x represents a discrete random variable
b) Specify the probability distribution for x
c) Find P(x-5)
d) Find P(x < 5)
e) Find E(x) and interpret the result
f) Is it likely to observe a hurricane after the 15th tropical storm of the season? Explain
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3. 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, part of the researchers' analysis included a graphic showing the sequence number of tropical storms within a season that are most likely to develop into a hurricane. Data for 67 hurricanes are summarized in the table. Let x represent the sequence number of a Florida tropical storm within a season that develops into a hurricane ence Number 10 12 13 14 15 a) Explain why x represents a discrete random variable b) Specify the probability distribution for x c) Find P(x-5) d) Find P(x < 5) e) Find E(x) and interpret the result f) Is it likely to observe a hurricane after the 15th tropical storm of the season? Explain

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check_circleAnswer
Step 1

a.

Explain the reason behind representing x as discrete random variable:

Discrete random variable:

If the variable X takes finite or countable values, then the variable X is said to be discrete.

The data represents the values of number of hurricanes developed corresponding to the sequence number of tropical storms within a season.

Consider the variable x represents the sequence number of tropical storms within a season.

The variable sequence number of tropical storms within a season takes the countable or finite values. The sequence numbers of tropical storms within a season are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 22.

Hence, the variable sequence number of tropical storms within a season is said to be discrete.

Step 2

Construct 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 xi = (Number of hurricanes developed for that particular xi)/(Total number of hurricanes).

The probabilities for the values x = 1, 2, 3, 4, 5, 6 is obtained below:

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Step 3

Construct the probability distribution for the variable x.

The probabilities for the v...

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