Questions: Question 5 10 pts Given a uniform probability distribution with a minimum of 5 and a maximum of 15 . Calculate the probability x=>12. Enter answer with 1 decimal. Note; If the answer is 0.7, include the zero before the decimal. Question 6 10 pts Given a uniform probability distribution with a minimum of 5 and a maximum of 15. Calculate the probability x<9. Enter answer with 1 decimal. Note; If the answer is 0.7, include the zero before the decimal.

Solution Steps

Given a uniform distribution with a minimum of \( a = 5 \) and a maximum of \( b = 15 \), we need to find the probability that \( x \) is greater than or equal to \( 12 \).

The probability can be calculated using the formula:

\[ P(x \geq 12) = \frac{b - 12}{b - a} \]

Substituting the values:

\[ P(x \geq 12) = \frac{15 - 12}{15 - 5} = \frac{3}{10} = 0.3 \]

Next, we calculate the probability that \( x \) is less than \( 9 \).

The probability can be calculated using the formula:

\[ P(x < 9) = \frac{9 - a}{b - a} \]

Substituting the values:

\[ P(x < 9) = \frac{9 - 5}{15 - 5} = \frac{4}{10} = 0.4 \]

Final Answer