Q. 77 A subway train arrives every eig... [FREE SOLUTION]

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Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 魅影直播 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 5: Q. 77 (page 353)

A subway train arrives every eight minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution. a. Define the random variable. X = ___ b. X ~ _ c. Graph the probability distribution. d. f(x) = _ e. 渭 = _ f. 蟽 = _____ g. Find the probability that the commuter waits less than one minute. h. Find the probability that the commuter waits between three and four minutes. i. Sixty percent of commuters wait more than how long for the train? State this in a probability question, similarly to parts g and h, draw the picture, and find the probabilit

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Measurement of variables

As per basis of provided information , X is the time length commuter that wait for a train

Uniform distribution of random variable X is

$X = U (0, 8)$

c. The probability distribution is

_{$\begin{array}{rcl} f (x) & = & \frac{1}{b - a} \\ = & \frac{1}{8 - 0} \\ = & \frac{1}{8} \end{array}$}

So, the graph is

The calculation of part c is

$f (x) = \{\begin{cases} \frac{1}{8} \\ 0 \end{cases} 0 < x < 8 o i s f o r o t h e r w i s e$

The mean value is

$\begin{array}{rcl} 渭 & = & \frac{a + b}{2} \\ = & \frac{0 + 18}{2} \\ = & 8 / 2 \\ = & 4 \end{array}$

The value of standard deviation

$\begin{array}{rcl} 蟽 & = & \frac{\sqrt{{(b - a)}^{2}}}{12} \\ 蟽 & = & \frac{\sqrt{{(8 - 0)}^{2}}}{12} \\ = & 2.31 \end{array}$

$P (x < 1) = b a s e 脳 h e i g h t = (1 - 0) 脳 \frac{1}{8} = 0.125$

Calculation of variables

h. The calculation

$P (3 < x < 4) = b a s e 脳 h e i g h t \begin{array}{rcl} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} (4 - 3) 脳 \frac{1}{8} \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} 0 \end{array} \begin{array}{rcl} . \end{array} \begin{array}{rcl} 125 \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} \end{array}$

i. The calculation of probability

$\begin{array}{rcl} P (x > k) = b a s e 脳 h e i g h t \\ 0.60 & = & (8 - k) 脳 \frac{1}{8} \\ k & = & 3.2 \end{array}$

The curve of the probability

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Short Answer

Step by step solution

Measurement of variables

Calculation of variables

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