Step-by-step explanation:
Since we are asked to round all answers to three decimal places, we will use the rounded values in our calculations.
To find the probability for each case, we need to calculate the length of the interval divided by the length of the total range.
1. The probability that the number will be exactly 18 is 0. Since the number is continuous, the probability of selecting a single value is zero.
2. The probability that the number will be between 18 and 20, inclusive, is (20 - 18.3) / (24.3 - 16.3) = 1.7 / 8 = 0.212.
3. The probability that the number will be between 18 and 20, exclusive, is (20 - 18) / (24.3 - 16.3) = 2 / 8 = 0.250.
4. The probability that the number will be less than 18 or greater than 20 is ((16.3 - 18) + (24.3 - 20)) / (24.3 - 16.3) = (-1.7 + 4.3) / 8 = 2.6 / 8 = 0.325.
5. The probability that the number will be less than 20 or greater than 18 is ((16.3 - 18.3) + (24.3 - 20)) / (24.3 - 16.3) = (-2 + 4.3) / 8 = 2.3 / 8 = 0.288.
Therefore, the probabilities are as follows:
- The probability that the number will be exactly 18 is 0.
- The probability that the number will be between 18 and 20, inclusive, is 0.212.
- The probability that the number will be between 18 and 20, exclusive, is 0.250.
- The probability that the number will be less than 18 or greater than 20 is 0.325.
- The probability that the number will be less than 20 or greater than 18 is 0.288.