A density curve of a uniform distribution takes the constant value k over the in

Question

A density curve of a uniform distribution takes the constant value k over the interval from 0 to 1.4 and is zero outside that range of values. This means that data described by this distribution take values that are uniformly spread between 0 and 1.4.

Please, can you show me how to solve this correctly ? Thank you :D

A density curve of a uniform distribution takes the constant value k over the interval from 0 to 1.4 and is zero outside that range of values. This means that data described by this distribution take values that are uniformly spread between 0 and 1.4. What does the total area under this density curve have to be? 714 What is the value of K? (Round your answer to three decimal places.) What percent of the observations lie above 0.8? (Round your answer to a whole number.) 428 X What percent of the observations lie below 0.2 (Round your answer to a whole number.) 856 What percent of the observations lie between 0.2 and 0.8? (Round your answer to a whole number.) X 428

Explanation / Answer

A density curve of a uniform distribution takes the constant value k over the interval from 0 to 1.4 and is zero outside that range of values. This means that data described by this distribution take values that are uniformly spread between 0 and 1.4

(A) area under curve has to be 1.

Interval of number in probability distribution = [0, 1.4]

Density of probability = 1/(1.4-0)=1/1.4 = 10/14 = 0.7143

(B) k = 0.714

(C)

Now the probability is (x > 0.8)
Interval of probability distribution of successful event = [0.8, 1.4] = 0.6
The probability ratio = 0.6*0.7143 = 0.4286 i.e. 43%

(D)

Now the probability is (x < 0.2)
Interval of probability distribution of successful event = [0, 0.2] = 0.2
The probability ratio = 0.2*0.7143 = 0.1429 i.e. 14%

(E)

Now the probability is (0.2 < x < 0.8)
Interval of probability distribution of successful event = [0.2, 0.8] = 0.6
The probability ratio = 0.6*0.7143 = 0.4286 i.e. 43%

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