The credit card industry has determined that about 65% of college student ls will be late making a minimum payment when paying their credit card every year atleast once. If 10 randomly selected students who own a credit card is selected what is the mean and standard deviation of college students who are late atleast once in a year?

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To find the mean and standard deviation, we can use the concept of a binomial distribution. In this case, the probability of a college student being late at least once in a year is given as 65% or 0.65.

The mean of a binomial distribution is calculated as the product of the number of trials (n) and the probability of success (p). In this case, the number of trials is 10 and the probability of success is 0.65. Therefore, the mean (μ) can be calculated as follows:

μ = n * p
= 10 * 0.65
= 6.5

So, the mean number of students who will be late at least once in a year is 6.5.

The standard deviation (σ) of a binomial distribution is calculated using the following formula:

σ = sqrt(n * p * (1 - p))

Substituting the given values into the formula, we get:

σ = sqrt(10 * 0.65 * (1 - 0.65))
= sqrt(10 * 0.65 * 0.35)
≈ 1.57

Therefore, the standard deviation of college students who will be late at least once in a year is approximately 1.57.