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
0.06 0 ≤ x < 1
0.16 1 ≤ x < 2
0.33 2 ≤ x < 3
0.69 3 ≤ x < 4
0.92 4 ≤ x < 5
0.99 5 ≤ x < 6
1 6 ≤ x

Calculate the following probabilities directly from the cdf
a. p(2), that is, P(X = 2)
b. P(X > 3)
c. P(2 ≤ X ≤ 5)
d. P(2 < X < 5)

the answer is 0.3175 hope that you ^w^

also you might actually want to put this picture up if you want people to solve it luckily i remember this question

1,589.63 in.^3

step-by-step explanation:

i hope this you : d

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation:

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.