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Chapter 4: Q42E (page 168)

The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean m, the actual temperature of the medium, and standard deviation. What would the value of s have to be to ensure that \(95\% \)of all readings are within \(.18\)of \(\mu \)?

Short Answer

Expert verified

The value for sigma has to be to ensure that \(95\% \) of all readings are within the given range are 0.05.

Step by step solution

01

Definition of Probability

A probability distribution is a mathematical function in probability theory and statistics that offers the odds of distinct potential scenarios for an experiment. It's a mathematical representation of random phenomena in terms of sample space and event probability.

02

Calculations for the determination of standard deviation.

As we already know that if the population distribution of a variable is (approximately) normal, then

(1.) Roughly \(68\% \)of the values are within \(1\) SD of the mean.

(2.) Roughly \(95\% \)of the values are within \(2\)SDs of the mean.

(3.) Roughly \(99.7\% \)of the values are within \(3\)SDs of the mean.

If the given distribution \(95\% \)of all readings is within \(0.1\)of \(\mu \), then

\(\begin{array}{l}2\sigma = 0.1\\\sigma = 0.05\end{array}\)

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Most popular questions from this chapter

Example \({\rm{4}}{\rm{.5}}\) introduced the concept of time headway in traffic flow and proposed a particular distribution for \({\rm{X = }}\) the headway between two randomly selected consecutive cars (sec). Suppose that in a different traffic environment, the distribution of time headway has the form

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If the temperature at which a certain compound melts is a random variable with mean value \({\rm{12}}{{\rm{0}}^{\rm{^\circ }}}{\rm{C}}\) and standard deviation \({{\rm{2}}^{\rm{^\circ }}}{\rm{C}}\), what are the mean temperature and standard deviation measured in \(^{\rm{^\circ }}{\rm{F}}\)? (Hint: \(^{\rm{^\circ }}{\rm{F = 1}}{\rm{.}}{{\rm{8}}^{\rm{^\circ }}}{\rm{C + 32}}{\rm{.}}\))

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