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Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 6: Q 52 (page 387)

Find the 80th percentile.

Short Answer

Expert verified

$The value of 80^{th} percentile is$ $60.3048$

Step by step solution

Given Information

Given that,

$X ~ N (54, 8)$

Where,

$渭 = 54$

$蟽 = 8$

Explanation

Now, $80^{th}$ percentile can be calculated

below:

$P (x < k) = P (\frac{x - 渭}{蟽} < \frac{k - 渭}{蟽})$

$0.80 = P (Z < \frac{k - 54}{8})$

$\frac{k - 54}{8} = 0.7881 \{\begin{array}{l} From standard \\ normal table \end{array}\}$

$k - 54 = 0.7881 脳 8$

$k = 6.3048 + 54$

localid="1649333427174" $k = 60.3048$

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Most popular questions from this chapter

In $2012$ , $1, 664, 479$ students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean $碌 = 496$ and a standard deviation $蟽 = 114$ . Let X = a SAT exam verbal section score in $2012$ . Then $X ~ N (496, 114)$ . Find the z-scores for $x_{1} = 325$ and $x_{2} = 366.21$ . Interpret each z-score. What can you say about $x_{1} = 325$ and $x_{2} = 366.21$ as they compare to their respective means and standard deviations ?

Suppose $X ~ N (鈥� 3, 1)$ . Between what $x$ values does $34.14 %$ of the data lie?

Suppose $x^{~} N (8, 9)$ . What value of $x$ is $0.67$ standard deviations to the left of the mean?

Suppose $X^{~} N (15, 3)$ . Between what $x$ values does $68.27 %$ of the data lie? The range of $x$ values is centered at the mean of the distribution (i.e., 15).

Suppose $X ~ N (鈥� 3, 1) .$ Between what $x$ values does $95.45 %$ of the data lie? The range of $x$ values is centered at the mean of the distribution(i.e., 鈥�3).

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91影视

Find the 80th percentile.

Short Answer

Step by step solution

Given Information

Explanation

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