mcba1234
contestada

For a normal distribution with a mean of 16 and a standard deviation of 3, find the 50th percentile. Can someone please explain how to solve this.

Respuesta :

IssacAsimov
The probability distribution of normal distribution is given by,

f(x) = [tex] \frac{1}{{ \sqrt{2 \pi \alpha ^{2} } }} e^{ \frac{-(x-a)^{2} }{2 \alpha^{2} } } [/tex]

Where a = mean = 16 and α = standard deviation = 3

In normal distribution, skewness is zero. That is, distribution is symmetric. 
Therefore, mean, median and mode coincide at a point in case of normal distribution.

50th percentile is same as median or mean or mode
Therefore, 50th percentile = 16
raphealnwobi

The 50th percentile of the normal distribution is 16.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation[/tex]

Given that:

μ = 16, σ = 3

From the normal distribution table, the 50th percentile corresponds with a z score of 0. Hence:

[tex]0=\frac{x-16}{3} \\\\x=16[/tex]

The 50th percentile of the normal distribution is 16.

Find out more at: https://brainly.com/question/16983854

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