# Suppose Y \sim N(\mu = 1, \sigma = 1). Compute the 75th percentile Q3 for this distribution.

## Question:

Suppose {eq}Y \sim N(\mu = 1, \sigma = 1) {/eq}. Compute the 75th percentile Q3 for this distribution.

## Third Quartile:

The third quartile is the data point below which 75% of the data lies. It is denoted by Q3 and also known as the 75th percentile as this data point is higher than 75% of the data value.

## Answer and Explanation:

{eq}\mu = 1\\ \sigma = 1 {/eq}

The 75th percentile is A.

P(X < A) = 0.75

P(Z < z) = 0.75

z = 0.67

We know:

{eq}X = \mu + Z\sigma {/eq}

So:

{eq}A = 1+ 0.67\times 1 = 1.67 {/eq}

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