A branch of a certain bank has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows: F(x) = 0 x < 0 0.08 0 ≤ x < 1 0.20 1 ≤ x < 2 0.40 2 ≤ x < 3 0.62 3 ≤ x < 4 0.83 4 ≤ x < 5 0.99 5 ≤ x < 6 1 6 ≤ x

1. P(x=2) = 0.39

2. P(x>3) =   0.33

3. P(2≤x≤5) = 0.58

4.  P(2<x<5) = 0.53

Step-by-step explanation:

1. P(x=2) = 0.39 (i.e the cdf of the range 2 ≤ x < 3)

2. P(x>3) =  1- P(x≤3) = 1 - 0.67 =  0.33

3. P(2≤x≤5) =  P(x≤5) -P(x≤2) = 0.97 - 0.39 = 0.58

4.  P(2<x<5) =  P(x<5) -P(x≤2) = 0.92 - 0.39 = 0.53

b. astronomers

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step-by-step explanation: