Assume that automobile accidents at a dangerous intersection occur according to a Poisson process at the rate of 3 accidents per week. Furthermore, the num- ber of people seriously injured in an accident has a Poisson distribution with mean 2 and is independent of the other accidents. Find the mean and standard deviation of the number of serious injuries over a one year's time.

The mean number of serious injuries over a one year's time is of 104 and the standard deviation is of 10.2

Step-by-step explanation:

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 interval. The standard deviation is the square root of the mean.

Find the mean and standard deviation of the number of serious injuries over a one year's time.

Per week, mean

A year has approximately 52 weeks, so, the mean is , and the standard deviation is

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation: