Q 26. Quick, click! An Internet reacti... [FREE SOLUTION]

91影视

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 837 pages

ISBN: 9781319113339

Chapter 6: Q 26. (page 372)

Quick, click! An Internet reaction time test asks subjects to click their mouse button as soon as a light flashes on the screen. The light is programmed to go on at a randomly selected time after the subject clicks 鈥淪tart.鈥� The density curve models the amount of time Y (in seconds) that the subject has to wait for the light to flash.
a) Find and interpret $P (Y > 3.75)$
b) What is $渭 Y$ ? Explain your answer.
c) Find the value of k that makes this statement true: $P (Y 鈮� k) = 0.38$

Short Answer

Expert verified

a) $0.3125 0 r 31.25 %$

b) $3$

c) $2.52$

Step by step solution

Step 1. Given information.

The density curve models the amount of timeY (in seconds) that the subject has to wait for the light to flash.

Step 2. Find and interpret.

The distribution is modeled by a uniform distribution on the interval fro $1$ seconds to $5$ seconds.

The density curve of distribution is

$f (x) = \frac{1}{b - a} = \frac{1}{5 - 1} = \frac{1}{4} = 0.25$

The probability

$P (Y > 3.75) = (5 - 3.75) 脳 \frac{1}{4} = 1.25 脳 \frac{1}{4} = \frac{5}{4} 脳 \frac{1}{4} = \frac{5}{16} = 0.3125 o r 31.25 %$

Step 3. Find the value of μY.

The uniform distribution is perfectly symmetric, which implies that the mean lies exactly in the middle of the distribution. The mean is then the value exactly in the middle of the boundaries of the interval on which the uniform distribution is defined and thus the mean can be determined as the average of the two boundaries.

$渭 = \frac{a + b}{2} = \frac{1 + 5}{2} = \frac{6}{2} = 3$