Se sabe que el 20% de todas las personas a quienes se administra cierto medicamento se siente muy mal en 2 minutos; encuentra la probabilidad de que entre 14 personas a las que se les administra este medicamento: a) A lo sumo 2 se sientan muy mal en dos minutos b) Por lo menos 5 se sientan muy mal en dos minutos c) De 2 a 4 se sientan muy mal en dos minutos

a) 0.4481

b) 0.1298

c) 0.6722

Step-by-step explanation:

English Translation

It is known that 20% of all people given a certain medicine feel very bad in 2 minutes; Find the probability that among 14 people who are given this medicine:

a) At most 2 feel very bad in two minutes

b) At least 5 feel very bad in two minutes

c) From 2 to 4 they feel very bad in two minutes

Solution

This is a binomial distribution problem

A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.

It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure.

The outcome of each trial/run of a binomial experiment is independent of one another.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 14

x = Number of successes required

p = probability of success = probability of feeling bad after taking the medicine = 20% = 0.20

q = probability of failure = probability of NOT feeling bad after taking the medicine = 1 - 0.20 = 0.80

a) At most 2 feel very bad in two minutes

P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)

= 0.04398046511 + 0.15393162789 + 0.25013889532 = 0.44805098832 = 0.4481

b) At least 5 feel very bad in two minutes

P(X ≥ 5) = 1 - P(X < 5) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)]

= 1 - [0.04398046511 + 0.15393162789 + 0.25013889532 + 0.25013889532 + 0.17197049053] = 0.12983962583 = 0.1298

c) From 2 to 4 they feel very bad in two minutes

P(2 ≤ X ≤ 4) = P(X=2) + P(X=3) + P(X=4)

= 0.25013889532 + 0.25013889532 + 0.17197049053 = 0.6722482811 = 0.6722

Hope this Helps!!!

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!