Statistics I
COMPLEMENTARY MATERIAL
How to Calculate Probability Using Excel
1. Introduction
Excel formulas or statistical functions can be used to calculate probabilities. Any
statistical function in Microsoft Excel 2007 and 2010, or another version, can be
accessed in different ways, as indicated in Lab 1. We can click the insert function f
(x) icon and choose the statistical functions.
Another way is to use Formulas in the Excel options (left side of the toolbar) and
select statistical formulas:
And, finally, there is another way to insert a function using Shift + F3 that shows
the following dialog box in which the Statistics category is selected
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2. Calculation of probabilities in discrete random variables: Binomial
There are several formulas or functions related to the calculation of probabilities
associated with the binomial distribution. In particular:
BINOM.CRIT
DISTR.BINOM
2.1 BINOM.CRIT
This function allows to calculate the lowest value whose accumulated binomial
probability is equal to a probability taken as critical value, given a number of tests
(sample size) and a probability of success in each test.
 Ensayos: the sample size or the number of results that could be a success or a
failure
 Prob_éxito: probability of favorable results
 Alfa: critical value
The result is the value that has a cumulative probability equal to or greater than
the Alpha value.
Example:
This function is used in QC (Quality Control) applications. For example, to
determine the largest number of defective parts that a washing machine assembly
line can produce without having to reject the whole lot. Data: 20 trials with a
probability of success of 0.6 and a critical value of 85%.
BINOM.CRIT(20;0,6;0,85) = 14
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2.2 DISTRIB.BINOM
This function results in the probability of a discrete random variable following a
binomial probability distribution.
 Núm_éxito: Number of favorable or successful results of the experiment
 Ensayos: sample size or the number of results that can result as a success or a
failure
 Prob_éxito: probability that the result of the experiment is favorable
 Acumulado: represents the form of the distribution, TRUE for cumulative or
FALSE distribution function for probability mass function.
Example:
The probability that a student will bring his laptop to class is 0.25. If there are 20
students in a class, calculate the following probabilities:
a) What is the probability that exactly 7 students bring the laptop to class?
P(n=20; p=0,25; x=7)
DISTR.BINOM(7; 20; 0,25; 0) = 0,1124
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b) What is the probability that at most 7 students will bring the laptop?
P (n=20; p=0,25; x<=7)
DISTR.BINOM(7; 20; 0,25; 1) = 0,8982
c) What is the probability of less than 6 students bringing it?
P (n=20; p=0,25; x<6) = P (n=20; p=0,25; x<=5)
DISTR.BINOM(5; 20; 0,25; 1) = 0,6172
d) What is the probability that more than 7 students will come with a laptop?
P (n=20; p=0,25; x>7) = P (n=20; p=0,25; x<=6)
1 - DISTR.BINOM(6; 20; 0,25; 1) = 1 - 0,785781948 = 0,214218052
e) What is the probability that at least 6 students will come with their laptop to
class?
P(n=20; p=0,25; x>=6) = P(n=20; p=0,25; x<5) = 1 - P(n=20; p=0,25; x>=5)
1 - DISTR.BINOM(5; 20; 0,25; 1) = 1 - 0,617172654 = 0,382827346
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3. Calculation of probabilities in continuous random variables: Normal
There are several formulas and functions related to the calculation of probabilities
associated with the Normal distribution. In this case there are the following:
DISTR.NORM
DISTR.NORM.INV
NORMALIZACIÓN
DISTR.NORM.ESTAND
DISTR.NORM.ESTAND.INV
3.1. DISTRIB.NORM
This function calculates the probability associated with a random variable that is
distributed Normal, given the mean and standard deviation of the population.




X: value to be used to calculate the probability
Media: mean of the distribution
Desv_estándar: standard deviation
Acum: logical value that defines the shape of the distribution (TRUE for
cumulative probability and FALSE for the probability distribution function).
Example:
The annual profit of a company can be approximated by a normal distribution with
mean 170 thousand of euros and standard deviation 800 euros. Therefore, the
annual benefit (measured in thousands of euros) follows a N(170, 0.8). Calculate
the following probabilities:
a) What is the probability that the benefit will be between 168 and 171 thousand
euros?
DISTR.NORM(171; 170; 0,8; 1) - DISTR.NORM(168; 170; 0,8; 1) =
0.894350226 – 0.006209665 = 0,888140561
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b) What is the probability that the benefit will be less than 169,500 euros?
DISTR.NORM(169,5; 170; 0,8; 1) = 0,265985529
c) What is the probability that the benefit will exceed 172 thousand euros?
1 - DISTR.NORM(172; 170; 0,8; 1) = 1 - 0,993790335 = 0,006209665
3.2. DISTRIB.NORM.INV
DISTR.NORM.INV:
This function returns the value of the Normal random variable distribution from a
specific probability, mean, and standard deviation.
 Probabilidad: value of the probability for which you want to calculate the
value of the associated variable.
 Media: average distribution parameter.
 Desv_estándar: standard deviation distribution parameter.
Example
Following the previous example of the annual benefit (measured in thousands of
euros) N (170, 0.8) distributed, calculate:
d) What is the benefit surpassed, at most, in 10% of the years? And for 5% of the
years?
DISTR.NORM.INV(0,9; 170; 0,8) = 171,0252413
DISTR.NORM.INV(0,95; 170; 0,8) = 171,3158829
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3.3. STANDARDIZATION
This function calculates the standardized values (z-value or z scores):
NORMALIZACION(x; media; desv_estándar)
 X: value you want to normalize.
 Media: mean of the distribution
 Desv_estándar: standard deviation of the distribution
Example
Following the previous example of the annual benefit (measured in thousands of
euros) N(170, 0.8) distributed, calculate:
e) What is the standardized value of a benefit of 169.5 thousand euros?
NORMALIZACION(169,5; 170; 0,8) = -0,625
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3.4. DISTRIB.NORM.ESTAND
This function calculates the value of the probability corresponding to a z score.
Example:
The number of international trips made to the semester by the manager of a
multinational company can be approximated by a normal distribution of average 7
and standard deviation 2 trips. Therefore, the number of international trips follows
a N(7, 2). Using the Normal (0, 1) distribution, calculate:
a) What is the probability that the manager makes between 5 and 8 trips?
DISTR.NORM.ESTAND(0,5) 0,158655254 = 0,532807207
DISTR.NORM.ESTAND(-1)
=
0,691462461
–
As an alternative to this calculation could be used:
DISTR.NORM(8; 7; 2; 1) - DISTR.NORM(5; 7; 2; 1) = 0,691462461 – 0,158655254 =
0,532807207
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3.5 DISTRIB.NORM.ESTAND.INV
This function calculates the z score corresponding to a given probability
Example:
Following the example of the number of international trips made this semester by
the manager of a multinational company that follows a N(7, 2), calculate:
b) What is the number of trips that you would have to do at least to not exceed
more than 2% of the semesters?
DISTR.NORM.ESTAND.INV(0,98) = 2,053748911
c) What is the minimum number of trips that would have been necessary to
perform to not exceed more than 2.5% of the semesters? And at 5% and 10%?
DISTR.NORM.ESTAND.INV(0,975) = 1,959963985
DISTR.NORM.ESTAND.INV(0,95) = 1,644853627
DISTR.NORM.ESTAND.INV(0,9) = 1,281551566
This formula is very useful for finding the critical values to use in the construction
of confidence intervals.
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