Question

Suppose the reaction temperature X (in °C) in a certain chemical process has a uniform distribution with A = −9 and B = 9. (a) Compute P(X < 0). (No Response) 0.5 (b) Compute P(−4.5 < X < 4.5). (No Response) 0.5 (c) Compute P(−7 ≤ X ≤ 8). (Round your answer to two decimal places.) (No Response) 0.83 (d) For k satisfying −9 < k < k + 4 < 9, compute P(k < X < k + 4). (Round your answer to two decimal places.) (No Response) 0.22

Answer 1

A. P(x<0)=0,5

B. P(-4,5<x<4,5)=0,5

C. P(-7<x<8)=0,83

D. P(k<x<k+4)=0,22

Explanation:

A. I hope that you need the reason why those answer are correct.

In a uniform distribution of probability, the probability of P(a<x<b) can be found as follows:

P(a<x<b)= (b-a)/B-A

where A,B are the limits of the function given A=-9, B=9. Because -9<x<9, then P(x<0)=P(-9>x>0) and now we use the formula:

P(-9<x<0)= 0-(-9)/( 9-(-9) )

P(-9<x<0)= 9/18 =0,5

B. We proceed using the formula as before:

P(-4,5<x<4,5)= (4,5-(-4,5)) / 18

P(-4,5<x<4,5)= 9/18 =0,5

C. And again, we use the formula:

P(-7<x<8)= (8-(-7)) / 18

P(-7<x<8)= 15/18 =0,8333... =0,83

D. This question could seem different because of the interval given there, let´s analyse it:

The inequality -9<k<k+4<9 it´s just a form to say that there is a probability for P(x<k) and P(x<k+4) because both k and k+4 belongs to the interval where the function is defined uniform. Now the question asks us, what is P(k<x<k+4), for all k that fills -9<k<k+4<9?

Because they fill -9<k<k+4<9, both of them belongs to [-9,9], then we can use the formula:

P(k<x<k+4)= k+4-(k) / 18

P(k<x<k+4)= 4/18 =0,2222... =0,22