22. According to ghost hunters, large cities have, on average, 9 haunted houses each. As far as we know, it is unpredictable which houses will be haunted; and just because one house is haunted, that does not mean any of its neighbors will or will not be haunted. a) What is the standard deviationof the number of haunted houses in a large city? b) What is the probability that 5or fewerhaunted houses will be found in a city?

a) The standard deviation is 3.

b) 11.56% probability that 5 or fewer haunted houses will be found in a city

Step-by-step explanation:

We only have the mean number of events, and the events are independent. So we use the Poisson distribution 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, which is the same as the variance.

According to ghost hunters, large cities have, on average, 9 haunted houses each.

This means that

a) What is the standard deviation of the number of haunted houses in a large city?

The variance is the same as the mean, which is 9. The standard deviation is the square root of the variance, so it is 3.

b) What is the probability that 5 or fewer haunted houses will be found in a city?

11.56% probability that 5 or fewer haunted houses will be found in a city

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°