DISTRIBUCIONES DE PROBABILIDAD PARA V.A CONTINUAS:

...

(a) What is the probability that there are more than three calls in one-half hour?

(b) What is the probability that there are no calls within onehalf hour?

(c) Determine x such that the probability that there are no calls within x hours is 0.01.

6.-The distance between major cracks in a highway follows an exponential distribution with a mean of 5 miles. Determine:

(a) What is the probability that there are no major cracks in a 10-mile stretch of the highway?

(b) What is the probability that there are two major cracks in a 10-mile stretch of the highway?

(c) What is the standard deviation of the distance between major cracks?

7.-Suponga que los tiempos entre llegadas de buques al puerto de Valparaíso, se distribuyen exponencialmente con media 12h.Dado que acaba de llegar el primer buque, determinar la probabilidad de que el segundo buque llegue :

a) Dentro de las próximas 12h.

b) Dentro de las próximas 24h.

c) Entre 12 y 18h mas.

d) Luego de 3 días.

C) DISTRIBUCION NORMAL:

FDP:

[pic 7]

FDA:

No existe expresión analítica.

[pic 8]

Media y Varianza:

[pic 9]

Aplicaciones:

a) Tiempos para completar una tarea.

b) Stocks Returns- Retornos o rendimientos de acciones

c) Errores aleatorios en torno a un valor central.

Funciones de EXCEL para la FDP Normal:

- Probabilidad acumulada desde -[pic 10] hasta x :

DISTR.NORM ( X; μ ; σ ; VERDADERO)

- Valor de x que acumula una probabilidad “Prob Acum” desde 0 hasta x :

DISTR.NORM.INV ( Prob Acum ; μ ; σ )

[pic 11]

PROBLEMAS:

1.-A private equity firm is evaluating two alternative investments. Although the returns are random, each investment’s return can be described using a normal distribution. The first investment has a mean return of $2,000,000 with a standard deviation of $125,000. The second investment has a mean return of $2,275,000 with a standard deviation of $500,000:

a). How likely is it that the first investment will return $1,900,000 or less?

b) How likely is it that the second investment will return $1,900,000 or less?

2.-The sick-leave time of employees in a firm in a month is normally distributed with a mean of 100 hours and a standard deviation of 20 hours.

(a) What is the probability that the sick-leave time for next month will be between 50 and 80 hours?

(b) How much time should be budgeted for sick leave if the budgeted amount should be exceeded with a probability of only 10%?

3.-The tensile strength of paper is modeled by a normal distribution with a mean of 35 pounds per square inch and a standard deviation of 2 pounds per square inch.

(a) What is the probability that the strength of a sample is less than 40 lb/in2 ?

(b) If the specifications require the tensile strength to exceed 30 lb/in2, what proportion of the samples is scrapped?

4.-The weight of a sophisticated running shoe is normally distributed with a mean of 12 ounces and a standard deviation of 0.5 ounce.

(a) What is the probability that a shoe weighs more than 13 ounces?

(b) What must the standard deviation of weight be in order for the company to state that 99.9% of its shoes are less than 13 ounces?

(c) If the standard deviation remains at 0.5 ounce, what must the mean weight be in order for the company to state that 99.9% of its shoes are less than 13 ounces?