In Sweden, 10 people are struck by lightning every year, on average. Answer thefollowing questions about a given year in Sweden using a relevant approximation. (Assumeperson-to-person and day-to-day independence, and assume all months have the same lengthand the same chance of lightning.)a. Find the probability that a total of two people are struck by lightning during first fourmonths of the year. b.Say that a month is good is no one is struck by lightning, and bad otherwise. Find the probability that the year has 5 good and 7 bad months.

a) 19.85% probability that a total of two people are struck by lightning during first four months of the year.

b) 22.68% probability that the year has 5 good and 7 bad months

Step-by-step explanation:

We are going to use the Poisson distribution and the binomial distribition to solve this question.

Poisson distribution:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given time interval.

Binomial distribution:

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

a.Find the probability that a total of two people are struck by lightning during first four months of the year.

10 people during a year(12 months).

In 4 months, the mean is

This is P(X = 2).

19.85% probability that a total of two people are struck by lightning during first four months of the year.

b.Say that a month is good is no one is struck by lightning, and bad otherwise. Find the probability that the year has 5 good and 7 bad months.

Probability that a month is good.

P(X = 0), Poisson

The mean is

Find the probability that the year has 5 good and 7 bad months.

Now we use the binomial distribution, we want P(X = 5) when n = 12, p = 0.4346. So

22.68% probability that the year has 5 good and 7 bad months

2.56 is the width of the garden

step-by-step explanation:

step-by-step explanation: