An annexation suit against a county subdivision of 1200 residences is being considered by a neighboring city. If the occupants of half the residences object to being annexed, what is the probability that in a random sample of 10 at least 3 favor the annexation suit?

Probability that in a random sample of 10 at least 3 favor the annexation suit is 0.9453.

Step-by-step explanation:

We are given that an annexation suit against a county subdivision of 1200 residences is being considered by a neighboring city. The occupants of half the residences object to being annexed.

Also, a random sample of 10 residents is taken.

The above situation can be represented through Binomial distribution;

where, n = number of trials (samples) taken = 10 residents

            r = number of success = at least 3

           p = probability of success which in our question is probability that

                 residents favor the annexation suit, which is calculated as below;

p = = = 0.50

LET X = Number of residents favoring the annexation suit

So, it means X ~

Now, Probability that in a random sample of 10 at least 3 favor the annexation suit is given by = P(X 3)

 P(X 3)  = 1 - P(X < 3) = 1 - P(X 2)

               = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]

=

=

=

= =

                                      = 0.9453

Therefore, Probability that in a random sample of 10 at least 3 favor the annexation suit is 0.9453.

44

step-by-step explanation:

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40