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Distribución de Probabilidad Normal: Cálculo de Valores de Z, Ejercicios de Estadística Empresarial

Cómo calcular los valores de Z en una distribución normal de probabilidad. Se incluyen ejemplos con tablas y herramientas de cálculo como Excel. Se utiliza la distribución normal para determinar proporciones de valores de una variable aleatoria, como las alturas de niñas de tres años o los resultados de un examen.

Tipo: Ejercicios

2021/2022

Subido el 24/11/2022

juank-z
juank-z 🇪🇨

3 documentos

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NORMAL PROBABILITY DISTRIBUTION
The normal curve is bellshaped and has a single peak at the exact center of
the distribution.
The arithmetic mean, median, and mode of the distribution are equal and
located at the peak. ( SYMMETRIC )
The normal probability distribution is symmetrical about its mean.
Exactly half the area under the curve is to the right of the peak, and the other
half is to the left.
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NORMAL PROBABILITY DISTRIBUTION

The normal curve is bellshaped and has a single peak at the exact center of the distribution. The arithmetic mean, median, and mode of the distribution are equal and located at the peak. ( SYMMETRIC ) The normal probability distribution is symmetrical about its mean. Exactly half the area under the curve is to the right of the peak, and the other half is to the left.

Z VALUE STANDARDIZATION OF THE VALUES OF A VARIABLE WE WANT TO STUDY

r of nd other

**1. Graph of the equation must be greater than or equal to zero for all possible values of the random variable.

  1. Area under the curve equals 1.**

EXAMPLE:

x Z VALUES ( Z SCORES ) VARIANCE = 19.5 0 STANDARD DEVIATION = 22 0.402576489533011 MEAN = 29 1. 10 -1. 17 -0. Assuming μ = 19,5 & σ^2 = 38,5641, find the Z values for :

ARIANCE = 38.

TANDARD DEVIATION = 6.

EAN = 19.

Z values for :

THE Z TABLE AREA UNDER THE CURVE IS NECESSARY FOR CALCUL

 - 1) P ( Z < -1,4 ) 0. 
  • ROW : -1, OPTION 1 : WITH TABLES
  • COLUMN: 0,
  • Z VALUE = -1. - 2) P ( Z > 1,85 ) 0.
    • ROW : 1, OPTION 1 : WITH TABLES
    • COLUMN: 0,
  • Z VALUE = 1.
    • P ( Z < 1,85 ) = 0.
        1. P ( Z BETWEEN 0,5 & 2,25) 0.
          • 1ST CALCULATE AREA FOR Z < 0, OPTION 1 : WITH TABLES - 0.
        • 2ND CALCULATE AREA FOR Z < 2, - 0. - ASSUMING AVERAGE = 0 & STANDARD DEVIATION =

URVE IS NECESSARY FOR CALCULATIONS!!!!!

1) P ( Z < -1,4 ) 0.

OPTION 2 : WITH EXCEL ( NORMSDIST())

2) P ( Z > 1,85 ) 0.

OPTION 2 : WITH EXCEL ( NORMSDIST())

P ( Z < 1,85 ) = 0.

3) P ( Z BETWEEN 0,5 & 2,25) 0.

OPTION 2 : WITH EXCEL ( NORMSDIST())

1ST CALCULATE AREA FOR Z < 0,

2ND CALCULATE AREA FOR Z < 2,

= 0 & STANDARD DEVIATION = 1

NORMDIST

X

MEAN

STANDARD DEVIATION

CUMMULATIVE = 1

1 ) P ( X < 35 )

ANSWER

2 ) P ( BETWEEN 35 & 40 )

ANSWER

A pediatrician obtains the heights of her 200 three-year-old female patients. The heights are approximately normally distributed, with mean 38.72 inches and standard deviation 3.17 inches.

  1. Use the normal model to determine the proportion of the 3-year-old females that have a h
  2. Compute the probability that a randomly selected 3-year-old female is between 35 and 40

The scores on a test are normall deviation of 6. Grades are assigned so that the top What is the lowest score a student c male patients. n 38.72 inches -year-old females that have a height less than 35 inches. d female is between 35 and 40 inches tall, inclusive.

ADDITIO

RCISE