Suppose x is a uniform random variable with c = 40 and d = 50. Find the probability that a randomly selected observation exceeds 46
To find the probability that a randomly selected observation from a uniform random variable exceeds 46, we need to determine the range of values for the random variable.
Given that the random variable x is uniformly distributed between c = 40 and d = 50, we know that the entire range of possible values for x is the interval [40, 50].
To find the probability that x exceeds 46, we need to calculate the relative length of the interval [46, 50] with respect to the total interval [40, 50].
The length of the interval [46, 50] is obtained by subtracting the lower bound from the upper bound: 50 - 46 = 4.
The length of the total interval [40, 50] is obtained by subtracting the lower bound from the upper bound: 50 - 40 = 10.
Therefore, the probability that a randomly selected observation from the uniform random variable x exceeds 46 is given by the ratio of the length of the interval [46, 50] to the length of the total interval [40, 50]:
P(x > 46) = (length of [46, 50]) / (length of [40, 50]) = 4 / 10 = 0.4
Thus, the probability that a randomly selected observation exceeds 46 is 0.4 or 40%.
To find the probability that a randomly selected observation exceeds 46, we need to calculate the area under the probability density curve to the right of 46.
Given that x is a uniform random variable with c = 40 and d = 50, the probability density function (PDF) is given by:
f(x) = 1 / (d - c)
In this case, d - c = 50 - 40 = 10, so the PDF simplifies to:
f(x) = 1 / 10
To find the probability, we need to integrate the PDF from 46 to 50, as the area under the curve represents the probability. Since the PDF is a constant, we can simply calculate the difference in the limits and multiply it by the PDF:
P(x > 46) = (50 - 46) * (1 / 10) = 4 / 10 = 2 / 5
Therefore, the probability that a randomly selected observation exceeds 46 is 2/5.
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It would be nice to know the men and standard deviation of the distribution of scores. What are c and d?
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