Questions: The graph of a uniform probability distribution is given below. From the figure, what is the probability that a randomly selected X is between 2.1 and 5.1? Give result accurate to at least 3 decimal places.

The graph of a uniform probability distribution is given below. From the figure, what is the probability that a randomly selected X is between 2.1 and 5.1? Give result accurate to at least 3 decimal places.
Transcript text: The graph of a uniform probability distribution is given below. From the figure, what is the probability that a randomly selected $X$ is between 2.1 and 5.1? Give result accurate to at least 3 decimal places. $\square$
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Solution

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Solution Steps

Step 1: Identify the range of the uniform distribution

The uniform distribution is defined over the interval [1, 7].

Step 2: Determine the height of the uniform distribution

The height of the uniform distribution is given as 1/7.

Step 3: Calculate the length of the interval of interest

The interval of interest is between 2.1 and 5.1. The length of this interval is: \[ 5.1 - 2.1 = 3 \]

Step 4: Calculate the probability

The probability of a uniform distribution over an interval is the length of the interval multiplied by the height of the distribution: \[ \text{Probability} = \text{Length of interval} \times \text{Height} \] \[ \text{Probability} = 3 \times \frac{1}{7} = \frac{3}{7} \approx 0.429 \]

Final Answer

The probability that a randomly selected \( X \) is between 2.1 and 5.1 is approximately 0.429.

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