Answer:
The probability that exactly 6 out of 10 randomly selected bank customers make a deposit into a savings account is approximately 0.2001.
Step-by-step explanation:
We can use the binomial distribution to solve this problem. The binomial distribution is a discrete probability distribution that describes the number of successes in a sequence of independent trials, each of which has a binary outcome (success or failure). In this case, the success is defined as a customer making a deposit into a savings account. The probability of success is 0.70, and the probability of failure is 0.30. We are interested in the probability that exactly 6 out of 10 randomly selected bank customers make a deposit into a savings account. This can be calculated using the following formula:
P(k) = (n choose k) * p^k * (1-p)^(n-k)
where:
P(k) is the probability of k successes
n is the number of trials
k is the number of successes
p is the probability of success
1-p is the probability of failure
In this case, we have:
n = 10
k = 6
p = 0.70
1-p = 0.30
Plugging these values into the formula, we get:
P(6) = (10 choose 6) * 0.70^6 * 0.30^4
P(6) ≈ 0.2001
Therefore, The probability that exactly 6 out of 10 randomly selected bank customers make a deposit into a savings account is approximately 0.2001.