Is the number 17 a prime or composite number?

Since 1851, exactly 119 hurricanes have hit Florida (this includes the years 1851 and 2019),—only direct hits by hurricanes are

alukav5142 [94]

Answer:

There is a 0.58% probability of Florida being struck by four or more hurricanes in the same year.

Step-by-step explanation:

Since we have only the mean during the interval, we can solve this problem using the Poisson probability distribution.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

Poisson probability distribution

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

$e = 2.71828$ is the Euler number

$\mu$ is the mean in the given time interval.

In this problem, we have that:

Since 1851, exactly 119 hurricanes have hit Florida (this includes the years 1851 and 2019). Counting 1851 and 2019, there are 169 years in this interval. This means that $\mu = \frac{119}{169} = 0.704$

If the probability of hurricane strikes has remained the same since 1851, what is the probability of Florida being struck by four or more hurricanes in the same year?

This is $P(X \geq 4)$ .

Either Florida is struck by less than four hurricanes in a given year, or it is struck by 4 or more. The sum of these probabilities is decimal 1.

$P(X < 4) + P(X \geq 4) = 1$

$P(X \geq 4) = 1 - P(X < 4)$

In which

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)$

So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-0.704}*(0.704)^{0}}{(0)!} = 0.4946$

$P(X = 1) = \frac{e^{-0.704}*(0.704)^{1}}{(1)!} = 0.3482$

$P(X = 2) = \frac{e^{-0.704}*(0.704)^{2}}{(2)!} = 0.1226$

$P(X = 3) = \frac{e^{-0.704}*(0.704)^{3}}{(3)!} = 0.0288$

$P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.4946 + 0.3482 + 0.1226 + 0.0288 = 0.9942$

Finally

$P(X \geq 4) = 1 - P(X < 4) = 1 - 0.9942 = 0.0058$

There is a 0.58% probability of Florida being struck by four or more hurricanes in the same year.

7 0

3 years ago

Reagan can walk 24 dogs in 8 hours. How many dogs can Regan walk in 10 hours?

KengaRu [80]

Answer:

30

Step-by-step explanation:

He is walking 3 dogs an hour

3 0

4 years ago

Read 2 more answers

Suppose I claim that the average monthly income of all students at college is at least $2000. Express H0 and H1 using mathematic

pishuonlain [190]

Answer:

For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:

Null hypothesis (H0): $\mu \geq 2000$

Alternative hypothesis (H1): $\mu$

And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no

Step-by-step explanation:

For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:

Null hypothesis (H0): $\mu \geq 2000$

Alternative hypothesis (H1): $\mu$

And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no

7 0

3 years ago

G<br> What is the value of f(x) when X=-3?<br> f(x)=-2x-3<br> f-3)=

Black_prince [1.1K]

Answer:

f(-3)=3

Step-by-step explanation:

We know that f(x)=-2x-3. In order to find f(-3), we simply need to substitute x with -3.

Thus, we have:

=-2(-3)-3

=6-3

=3

5 0

3 years ago

Read 2 more answers

Evaluate C7, 5).<br><br> A. 21<br><br> B. 42<br><br> C. 1,008

faltersainse [42]

<h3>Answer: A. 21</h3>

=======================================

C(n, r) = (n!)/(r!*(n-r)!) is the combination formula

C(7, 5) = (7!)/(5!*(7-5)!)

C(7, 5) = (7!)/(5!*2!)

C(7, 5) = (7*6*5!)/(5!*2!)

C(7, 5) = (7*6)/(2!) ..... note the "5!" terms divided and canceled

C(7, 5) = (7*6)/(2*1)

C(7, 5) = 42/2

C(7, 5) = 21

4 0

4 years ago