Cans 6 cm 3 cm and 9 cm make a triangle

The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it

brilliants [131]

Answer:

(a) 11.25 and 1.68

(b) 0.1651

(c) 0.3903

(d) 0.6865

Step-by-step explanation:

We are given that GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 75% of the cases and suppose the 15 cases reported today are representative of all complaints.

This situation can be represented through Binomial distribution as;

$P(X=r)= \binom{n}{r}p^{r}(1-p)^{n-r} ; x = 0,1,2,3,....$

where, n = number of trials (samples) taken = 15

r = number of success

p = probability of success which in our question is % of cases in

which customer problems are resolved on the same day, i.e.;75%

So, here X ~ $Binom(n=15,p=0.75)$

(a) Expected number of problems to be resolved today = E(X)

E(X) = $\mu$ = n * p = 15 * 0.75 = 11.25

Standard deviation = $\sigma$ = $\sqrt{n*p*(1-p)}$ = $\sqrt{15*0.75*(1-0.75)}$ = 1.68

(b) Probability that 10 of the problems can be resolved today = P(X = 10)

P(X = 10) = $\binom{15}{10}0.75^{10}(1-0.75)^{15-10}$

= $3003*0.75^{10} *0.25^{5}$ = 0.1651

(c) Probability that 10 or 11 of the problems can be resolved today is given by = P(X = 10) + P(X = 11)

= $\binom{15}{10}0.75^{10}(1-0.75)^{15-10}+\binom{15}{11}0.75^{11}(1-0.75)^{15-11}$

= $3003*0.75^{10} *0.25^{5} + 1365*0.75^{11} *0.25^{4}$ = 0.3903

(d) Probability that more than 10 of the problems can be resolved today is

given by = P(X > 10)

P(X > 10) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

= $\binom{15}{11}0.75^{11}(1-0.75)^{15-11}+\binom{15}{12}0.75^{12}(1-0.75)^{15-12} + \binom{15}{13}0.75^{13}(1-0.75)^{15-13}+\binom{15}{14}0.75^{14}(1-0.75)^{15-14} + \binom{15}{15}0.75^{15}(1-0.75)^{15-15}$

= $1365*0.75^{11} *0.25^{4} + 455*0.75^{12} *0.25^{3}+105*0.75^{13} *0.25^{2} + 15*0.75^{14} *0.25^{1}+1*0.75^{15} *0.25^{0}$

= 0.6865

3 0

3 years ago

en una balansa de platillos esta equilibrada, en uno de los platillos hay una piedra, una pesa de un noveno kilogramos y la otra

Komok [63]

Se escribe una equacion y se resolve.

Vamos a usar x para representar el peso de la piedra.

En en platillo que tiene la piedra, el peso total es: x + 1/9 + 2/3

En el otro platillo: 1/2 + 1/3

La balanza esta equilibrada por eso los pesos en los platillos son iguales.

x + 1/9 + 2/3 = 1/2 + 1/3

x + 2/18 + 12/18 = 9/18 + 6/18

x + 14/18 = 15/18

x = 1/18

Respuesta: La piedra pesa un octavo de kilogramo.

3 0

3 years ago

Read 2 more answers

Rewrite as a simplified fraction. 3. 5 =?<br> 5 repeats

True [87]

Answer:

32/9

Step-by-step explanation:

3 0

3 years ago

Write these in order of size starting<br>with smallest in<br>7m 750 cm 0.7m 77cm

MArishka [77]

Answer:

it's 0.7m, 77cm , 7m , 750 cm . hope I helped you .

5 0

3 years ago

What is the difference between the mean and the median of the following distribution?

natulia [17]

The definition of mean, is to add up all the numbers and divide it by how many numbers there are. So, in this case the mean would be 1+1+1+2+2+2+2+3+3+4+4+4+4+5+5+6+7+7+8+8+9 = 86. You would then take 86 and divide that by 21, and you would get 4.0
The definition of median states to find the middle of the numbers. So the median would be 4.
So you would just take 4 - 4 = 0.

0 would be correct.

8 0

3 years ago

Read 2 more answers