A survey of consumer finance found that 25.4% of credit-card-holding families hardly ever pay off the balance. Suppose a random sample of 20 credit-card-holding families is taken. Find the probabilities of each of the following results. Source: Statistical Abstract of the United States. 25. Exactly 6 families hardly ever pay off the balance. 26. Exactly 9 families hardly ever pay off the balance. 27. At least 4 families hardly ever pay off the balance. 28. At most 5 families hardly ever pay off the balance.

25. P(6) = 0.1721

26. P(9) = 0.0294

27.

28.

Step-by-step explanation:

When we have n identical and independent events with a probability p of success and (1-p) of fail, we have a Binomial distribution. So, the probability that x events are success is calculated as:

So, the probability that x families hardly ever pay off the balance follows a binomial distribution and it is calculated as:

where n is 20 and p is 0.254.

Then, the probability that exactly 6 families hardly ever pay off the balance is:

The probability that exactly 9 families hardly ever pay off the balance is:

The probability that at least 4 families hardly ever pay off the balance is:

So, using the same equation to find every probability, we get:

Finally, the probability that at most 5 families hardly ever pay off the balance is:

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step-by-step explanation:

step-by-step explanation: