The interest rates paid by 30 financial institutions on a certain day for money market deposit accounts are shown in the accompanying table.
Rate %  2  2.25  2.55  2.56  2.58  2.60  2.65  2.85 

Institutions  2  6  9  1  1  7  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.)
a)dividing each frequency with n=30 :
Rate %  P(X=x) 
2  0.067 
2.25  0.200 
2.55  0.300 
2.56  0.033 
2.58  0.033 
2.60  0.233 
2.65  0.067 
2.85  0.067 
b) probability that the interest rate paid by a financial institution chosen at random is less than 2.56% per year =(9+6+2)*100/30=0.567
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