using empirical formula a company is studying the number of daily debit card purchases. THere were 20 purchases and the probability of a debit card purchase is 0.5. what is the stadnard deviation of the number of debit card purchases
0.5
To calculate the standard deviation of the number of debit card purchases, we need to use the formula for the standard deviation of a binomial distribution.
The formula for the standard deviation of a binomial distribution is given by the square root of n * p * (1 - p), where n is the number of trials and p is the probability of success.
In this case, the number of trials (purchases) is 20, and the probability of a debit card purchase is 0.5.
Substituting these values into the formula, we get:
Standard Deviation = √(20 * 0.5 * (1 - 0.5))
Calculating further:
Standard Deviation = √(10 * 0.5 * 0.5)
Standard Deviation = √(2.5)
Therefore, the standard deviation of the number of debit card purchases is approximately 1.58 (rounded to two decimal places).