### Interest Rates and Probability DistributionThe interest rates paid by 30 financial institutions on a certain day for money market deposit accounts are displayed in the following table:| Rate % | 2 | 2.25 | 2.55 | 2.56 | 2.58 | 2.60 | 2.65 | 2.85 ||--------|----|------|------|------|------|------|------|------|| Institutions | 1 | 9 | 7 | 2 | 1 | 6 | 2 | 2 |Let the random variable $ X $ denote the interest rate per year paid by a randomly chosen financial institution on its money market deposit accounts.#### (a) Find the probability distribution associated with these data. *(Round your answers to three decimal places.)*| Rate % | $ P(X = x) $ ||--------|---------------|| 2 | || 2.25 | || 2.55 | || 2.56 | || 2.58 | || 2.60 | || 2.65 | || 2.85 | |#### (b) Find the probability that the interest rate paid by a financial institution chosen at random is less than 2.56% per year. *(Round your answer to three decimal places.)*\[ \text{Probability} = \] This exercise involves calculating the probability distribution of interest rates offered by various financial institutions and determining the likelihood of a particular event.

given data; Rate % 2 2.25 2.55 2.56 2.58 2.60 2.65 2.85 Institution 1 9 7 2 1 6 2 2X: the interest rate per year paid by a randomly chosen financial institution on its money market deposit accounts. (a) Rate % (X) P(X=x) 2 130≈0.033 2.25 930≈0.300 2.55 730≈0.233 2.56 230≈0.067 2.58 130≈0.033 2.60 630≈0.200 2.65 230≈0.067 2.85 230≈0.067 (b) P(X<2.56%)=P(X=2%)+P(X=2.25%)+P(X=2.55%)=130+930+730= 1730 or 0.567 (ANS: 0.567)