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Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset Vaia Explanations$ Math

OER 2018 Edition · 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

01

Given Information

Given that,

$X ~ N (54, 8)$

Where,

$μ = 54$

$σ = 8$

02

Explanation

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

below:

$P (x < k) = P (\frac{x - μ}{σ} < \frac{k - μ}{σ})$

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

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

$k - 54 = 0.7881 \times 8$

$k = 6.3048 + 54$

localid="1649333427174" $k = 60.3048$

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Most popular questions from this chapter

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.

Find the probability that it takes at least eight minutes to find a parking space.

a. 0.0001

b. 0.9270

c. 0.1862

d. 0.0668

In a normal distribution, x = 6 and z = –1.7. This tells you that x = 6 is ____ standard deviations to the ____ (right or left) of the mean.

Use the following information to answer the next four exercises: $X ~ N (54, 8)$

Find the probability that $x < 30$

What is the area to the right of three?

A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?

See all solutions

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