Enter Number of Occurrences (n) Enter probability of success (p) Enter Number of successes (k) Moment Number (t) (Optional)
         

Calculate the Z score using the Normal Approximation to the Binomial distribution given:

n = 10 and p = 0.4 with 3 successes

with and without the Continuity Correction Factor

The Normal Approximation to the Binomial Distribution Formula is below:

Z  =  X - np
  √np(1 - p)

Calculate nq to see if we can use the Normal Approximation:

Since q = 1 - p, we have n(1 - p) = 10(1 - 0.4)

nq = 10(0.6)

nq = 6

Since np and nq are both not greater than 5, we cannot use the Normal Approximation to the Binomial Distribution.

Calculate the mean μ (expected value)

μ  =  np

μ  =  10 x 0.4

μ = 4

Calculate the variance σ2

σ2  =  np(1 - p)

σ2  =  10 x 0.4 x (1 - 0.4)

σ2  =  4 x 0.6

σ2 = 2.4

Calculate the standard deviation σ

σ  =  √σ2 = √np(1 - p)

σ  =  √2.4

σ = 1.5492

Plug in values for Z score

Using the mean (np) = 4 and the standard deviation √np(1 - p) = 1.5492 and 3 successes calculated above, we can find our Z score

Z  =  3 - 4
  1.5492

Z  =  -1
  1.5492

Z = -0.6455

Calculate P(Z < -0.6455)

Using our z-score calculator for P(Z < -0.6455)

Calculate P(Z > -0.6455)

Using our z-score calculator for P(Z > -0.6455)

Now calculate the probabilities using the Continuity Correction Factor by subtracting 0.5:

Z  =  X - 0.5 - np
  √np(1 - p)

Z  =  3 - 0.5 - 4
  1.5492

Z  =  -1.5
  1.5492

Z = -0.9682

Calculate P(Z < -0.9682)

Using our z-score calculator for P(Z < -0.9682)

Calculate P(Z > -0.9682)

Using our z-score calculator for P(Z > -0.9682)

Final Answer

Z = -0.9682


You have 2 free calculationss remaining



What is the Answer?
Z = -0.9682
How does the Binomial Distribution Calculator work?
Free Binomial Distribution Calculator - Calculates the probability of 3 separate events that follow a binomial distribution. It calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness and kurtosis.
Also calculates the normal approximation to the binomial distribution with and without the continuity correction factor
Calculates moment number t using the moment generating function
This calculator has 4 inputs.

What 3 formulas are used for the Binomial Distribution Calculator?

q = 1 - p
f(k;n,p) = n! * pkqn - k/k!(n - k)!
Z = X - np/√np(1 - p)

For more math formulas, check out our Formula Dossier

What 10 concepts are covered in the Binomial Distribution Calculator?

binomial distribution
discrete probability distribution of the number of successes in a sequence of n independent experiments, with a success or failure outcome
continuity correction factor
the bridge between the continuous normal distribution and the discrete binomial
event
a set of outcomes of an experiment to which a probability is assigned.
factorial
The product of an integer and all the integers below it
mean
A statistical measurement also known as the average
moment
a function are quantitative measures related to the shape of the functions graph
probability
the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes
standard deviation
a measure of the amount of variation or dispersion of a set of values. The square root of variance
variance
How far a set of random numbers are spead out from the mean
Example calculations for the Binomial Distribution Calculator
  1. n=10, p=0.4, x=3

Binomial Distribution Calculator Video


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