A random variable follow a normal distribution with

Capriconian321

Capriconian321

Answered question

2022-08-08

A random variable follow a normal distribution with mean 12 and variance 2.5. Find upper quartile

Answer & Explanation

Don Sumner

Don Sumner

Skilled2023-05-23Added 184 answers

To find the upper quartile of a random variable following a normal distribution with a mean of 12 and a variance of 2.5, we can use the properties of the normal distribution.
The upper quartile, also known as the 75th percentile, is the value below which 75% of the data falls. In a standard normal distribution, the upper quartile corresponds to a z-score of approximately 0.674.
To find the upper quartile in terms of the original distribution, we need to convert this z-score back to the original units using the mean and standard deviation.
The standard deviation of a normal distribution is the square root of the variance. In this case, the standard deviation (σ) is √2.5.
The formula to convert a z-score to an actual value in the normal distribution is:
X=μ+zσ
where X is the actual value, μ is the mean, z is the z-score, and σ is the standard deviation.
Plugging in the values we have:
X=12+0.674·2.5
Calculating this expression:
X=12+0.674·1.5811
X=12+1.0667
X=13.0667
Therefore, the upper quartile of the random variable following the given normal distribution is approximately 13.0667.

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