SaiBook.us Statistics

Lesson

Title: Binomial distribution

Grade: 9-a Lesson: S4-L4

Explanation: Hello students, let us learn a new topic in statistics today with definitions, concepts, examples, and worksheets included.

Lesson:

Definition: Binomial distribution:

Binomial distribution is a probability distribution used in statistics that summarizes the likelihood that a value will take one of two independent values under a given set of parameters or assumptions.

n = number of experiments,

p = Probability of success in any experiment,

q= Probability of failures in any experiment,

x = number of successful trials.

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Explanation:

Applications of binomial distribution:

Finding the quantity of raw and used materials while making a product.
Taking a survey of positive and negative reviews from the group of people
By using the YES/ NO survey
To find the number of male and female students in a college.
The number of votes collected by a candidate in an election is counted based on 0 or 1 probability.

Definition: Mean and variance of binomial distribution:

The mean of the binomial distribution is np, and the variance of the binomial distribution is np (1 − p).
When p = 0.5, the distribution is symmetric around the mean.
When p > 0.5, the distribution is skewed to the left.
When p < 0.5, the distribution is skewed to the right.

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Explanation:

Properties of Binomial Distribution:

There are two possible outcomes: true or false, success or failure, yes or no.
There is ‘n’ number of independent trials or a fixed number of n times repeated trials.
The probability of success or failure remains the same for each trial.
Only the number of success is calculated out of n independent trials.
Every trial is an independent trial, which means the outcome of one trial does not affect the outcome of another trial.