Final answer:
The question discusses the probability distribution for a reaction temperature with a uniform distribution. The probability density function is constant between the lower and upper bounds of the distribution and zero outside it. The mean and standard deviation of the uniform distribution are also given.
Step-by-step explanation:
The probability density function (PDF) for a continuous uniform distribution is given by f(x) = 1 / (b - a) where a and b are the parameters of the distribution representing the lower and upper bounds, respectively. For a uniform distribution U(a, b), the PDF is constant between the interval [a, b] and zero outside this interval.
To answer the specific inquiries: For a continuous probability distribution, the probability P(x > 15) when 0 ≤ x ≤ 15 is zero, as it is outside the defined range; The area under f(x) when it is a continuous probability density function is always 1, signifying the total probability; The probability P(x = 7) or P(x = 10) for any specific value in a continuous distribution is always zero due to the infinitesimal width of a point; For P(x < 0), where the interval is between 0 and 5, the probability is again zero, as the value lies outside the interval of the distribution.
The theoretical mean μ of a uniform distribution U(a, b) is (a + b) / 2, and the standard deviation σ is (b - a) / sqrt(12). The graph of a uniform distribution is a rectangle with height 1 / (b - a).