6. Normal Distribution and Continuous Random Variables

Uniform Distribution

6. Normal Distribution and Continuous Random Variables

Uniform Distribution

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Multiple Choice

Shade the area corresponding to the probability listed, then find the probability.
$P of open paren 2 is less than X is less than 4 close paren$

Graph showing a uniform distribution with shaded area between x=2 and x=4, indicating the probability density. ; $P of open paren 2 is less than X is less than 4 close paren equals 0.25$

Graph showing a uniform distribution with a shaded area between x=2 and x=4, indicating the probability density. ; $P of open paren 2 is less than X is less than 4 close paren equals 0.25$

Graph showing a uniform distribution with shaded area between x=2 and x=4, indicating the probability density. ; $P of open paren 2 is less than X is less than 4 close paren equals 0.5$

Graph showing a uniform distribution with a shaded area between x=2 and x=4, indicating the probability density. ; $P of open paren 2 is less than X is less than 4 close paren equals 0.5$

Verified step by step guidance

Step 1: Identify the type of probability distribution. The graph provided represents a uniform probability density function, where the probability density is constant (0.25) over the interval [1, 5].

Step 2: Understand the problem. The goal is to find the probability that the random variable X falls within the interval (2, 4), denoted as P(2 < X < 4). This corresponds to the shaded green area in the graph.

Step 3: Recall the formula for calculating probabilities in a uniform distribution. The probability is calculated as the area under the curve within the specified interval. For a uniform distribution, this area is given by the product of the probability density and the width of the interval.

Step 4: Determine the width of the interval (2, 4). The width is calculated as the difference between the upper and lower bounds of the interval: width = 4 - 2 = 2.

Step 5: Multiply the probability density (0.25) by the width of the interval (2) to calculate the probability: P(2 < X < 4) = 0.25 × 2.

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Struggling with Statistics?

Shade the area corresponding to the probability listed, then find the probability. P(2<X<4)P\left(2<X<4\right)

Watch next

Uniform Distribution practice set

Shade the area corresponding to the probability listed, then find the probability.
$P of open paren 2 is less than X is less than 4 close paren$