   Chapter 8.4, Problem 41E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Reaction time Reaction time is normally distributed, with a mean of 0.7 sec and a standard deviation of 0.1 sec. Find the probability that an individual selected at random has a reaction time(a) greater than 0.9 sec.(b) less than 0.6 sec.(c) between 0.6 and 0.9 sec.

(a)

To determine

To calculate: The probability that an individual selected has a reaction greater than 0.9 sec if reaction time is normally distributed with mean 0.7 sec, and a standard deviation of 0.1 sec.

Explanation

Given Information:

Reaction time is normally distributed with mean 0.7 sec, and a standard deviation of 0.1 sec.

Formula used:

The z score for a normally distribution of x is,

z=xμσ

Where, μ is the mean and σ is the standard deviation.

Calculation:

Consider the mean is 0.7 sec and standard deviation 0.1 sec,

μ=0.7 and σ=0.1

Use the formula to calculate z score for a normally distribution of x is,

z=xμσ

Substitute 0.7 for μ, 0.1 for σ and 0.9 for x.

z1=0.90.70.1=2

As normal distribution is symmetric about mean 0.5.

So this implies,

Pr(z2)=0

(b)

To determine

To calculate: The probability that an individual selected has a reaction less than 0.6 sec if reaction time is normally distributed with mean 0.7 sec, and a standard deviation of 0.1 sec.

(c)

To determine

To calculate: The probability that an individual selected has a reaction between 0.6 sec and 0.9 sec if reaction time is normally distributed with mean 0.7 sec, and a standard deviation of 0.1 sec.

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