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 “Start.” 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 $μ Y$ ? Explain your answer.
c) Find the value of k that makes this statement true: $P (Y \leq k) = 0.38$

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

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

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.

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

Step 4. Find the value of k in P(Y≤k)=0.38

$P (Y \leq k) = 0.38 \frac{k - 1}{4} = 0.38 k - 1 = 1.52 k = 2.52$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find and interpret.

Step 3. Find the value of μY.

Step 4. Find the value of k in P(Y≤k)=0.38

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Logic and Functions

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.