Answer:
the probability that X is less than 4, P(X < 4), is approximately 0.273 (rounded to three decimal places).
Explanation:
To find the probability that X is less than 4, we need to calculate the cumulative distribution function (CDF) of the uniform distribution.
The uniform distribution is defined by the minimum value a and the maximum value b. In this case, X ~ U(1, 12), where a = 1 and b = 12.
The CDF of a uniform distribution is given by:
CDF(x) = (x - a) / (b - a)
Substituting the values a = 1 and b = 12 into the formula, we have:
CDF(x) = (x - 1) / (12 - 1)
= (x - 1) / 11
To find P(X < 4), we substitute x = 4 into the CDF formula:
P(X < 4) = CDF(4)
= (4 - 1) / 11
= 3 / 11
≈ 0.273
Therefore, the probability that X is less than 4, P(X < 4), is approximately 0.273 (rounded to three decimal places).