A home security system is designed to have a 99% reliability rate. Suppose that nine homes equipped with this system experience an attempted burglary. Find the probabilities of these events:. A. At least one alarm is triggered.
B. More than seven alarms are triggered.
C. Eight or fewer alarms are triggered.

a)

And replacing we got:

b)

And adding we got:

c)

And replacing we got:

Step-by-step explanation:

Let X the random variable of interest "numebr of times that an alarm is triggered", on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

Part a

We want to find this probability:

And replacing we got:

Part b

And adding we got:

Part c

And replacing we got:

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.