Questions: Answer the following: a. Find the uniform continuous probability for P(X<12) for U(0,50). Note: Round your answer to 2 decimal places. Probability b. Find the uniform continuous probability for P(X>800) for U(0,1,000). Note: Round your answer to 3 decimal places. Probability c. Find the uniform continuous probability for P(26<X<58) for U(19,63). Note: Round your answer to 4 decimal places. Probability

Solution Steps

To find the probability \( P(X < 12) \) for a uniform distribution \( U(0, 50) \), we use the formula for the probability of a uniform distribution:

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

where \( a = 0 \) and \( b = 50 \). Substituting \( x = 12 \):

\[ P(X < 12) = \frac{12 - 0}{50 - 0} = \frac{12}{50} = 0.24 \]

Thus, the probability is \( 0.24 \).

To find the probability \( P(X > 800) \) for a uniform distribution \( U(0, 1000) \), we can use the complementary probability:

\[ P(X > x) = 1 - P(X < x) \]

Calculating \( P(X < 800) \):

\[ P(X < 800) = \frac{800 - 0}{1000 - 0} = \frac{800}{1000} = 0.8 \]

Thus,

\[ P(X > 800) = 1 - 0.8 = 0.2 \]

The probability is \( 0.2 \).

To find the probability \( P(26 < X < 58) \) for a uniform distribution \( U(19, 63) \), we use the formula:

\[ P(a < X < b) = \frac{b - a}{d - c} \]

where \( c = 19 \) and \( d = 63 \). Substituting \( a = 26 \) and \( b = 58 \):

\[ P(26 < X < 58) = \frac{58 - 26}{63 - 19} = \frac{32}{44} = \frac{8}{11} \approx 0.7273 \]

Thus, the probability is approximately \( 0.7273 \).

Final Answer