Question

select the correct answer.
what is the missing probability in this probability distribution?

interval	0 - 10	11 - 20	21 - 30	31 - 40	41 - 50

a. 1.125
b. 0.119
c. 0.125
d. 0.012

Explanation:

Step1: Recall total probability rule

The sum of all probabilities in a probability distribution is \(1\). Let the missing probability be \(x\).

Step2: Sum the known probabilities

Sum of known probabilities: \(0.105 + 0.255 + 0.301 + 0.214\)
\(0.105+0.255 = 0.36\); \(0.36 + 0.301 = 0.661\); \(0.661 + 0.214 = 0.875\)

Step3: Solve for \(x\)

Using the total probability rule: \(0.875 + x = 1\)
So, \(x = 1 - 0.875 = 0.125\)? Wait, no, wait. Wait, let's recalculate the sum of known probabilities again. Wait, 0.105 + 0.255 is 0.36, 0.36 + 0.301 is 0.661, 0.661 + 0.214 is 0.875. Then 1 - 0.875 is 0.125? But wait, option B is 0.119. Wait, did I miscalculate? Wait, 0.105 + 0.255 = 0.36; 0.36 + 0.301 = 0.661; 0.661 + 0.214 = 0.875. Then 1 - 0.875 = 0.125. But option C is 0.125. Wait, maybe I made a mistake. Wait, let's check the numbers again. The intervals are 0-10 (0.105), 11-20 (0.255), 21-30 (x), 31-40 (0.301), 41-50 (0.214). So sum is 0.105 + 0.255 + x + 0.301 + 0.214 = 1. So adding the knowns: 0.105 + 0.255 = 0.36; 0.36 + 0.301 = 0.661; 0.661 + 0.214 = 0.875. So 0.875 + x = 1 => x = 0.125. But option C is 0.125. Wait, but the options have B as 0.119. Wait, maybe I misread the numbers. Wait, let's check the problem again. The probability for 31-40 is 0.301, 41-50 is 0.214. 0.105 + 0.255 is 0.36, 0.36 + 0.301 is 0.661, 0.661 + 0.214 is 0.875. 1 - 0.875 is 0.125. So the missing probability is 0.125, which is option C. Wait, but maybe I made a mistake in addition. Wait, 0.105 + 0.255: 0.1 + 0.25 = 0.35, 0.005 + 0.005 = 0.01, so 0.36. Correct. 0.36 + 0.301: 0.36 + 0.3 = 0.66, +0.001 = 0.661. Correct. 0.661 + 0.214: 0.661 + 0.2 = 0.861, +0.014 = 0.875. Correct. So 1 - 0.875 = 0.125. So the answer should be C. 0.125.

Wait, but the initial calculation I thought maybe B, but no, the sum is 0.875, so 1 - 0.875 is 0.125. So the missing probability is 0.125.

Answer:

C. 0.125