The charge-to-tap time (min) for carbon steel in one type of open hearth furnace is to be determined for each heat in a sample of size $n$. If the investigator believes that almost all times in the distribution are between 320 and $440,$ what sample size would be appropriate for estimating the true average time to within 5 min. with a confidence level of $95 \%$ ? A reasonable value for $s$ is $(440-320) / 4=30 .$ Thus$$n=\left[\frac{(1.96)(30)}{5}\right]^{2}=138.3$$since the sample size must be an integer, $n=139$ should be used. Note that estimating to within 5 min. with the specified confidence level is equivalent to a CI width of $10 \mathrm{min}$.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The charge-to-tap time (min) for carbon steel in one type of open hearth furnace is to be determined for each heat in a sample of size $n$. If the investigator believes that almost all times in the distribution are between 320 and $440,$ what
$$
n=\left[\frac{(1.96)(30)}{5}\right]^{2}=138.3
$$
since the sample size must be an integer, $n=139$ should be used. Note that estimating to within 5 min. with the specified confidence level is equivalent to a CI width of $10 \mathrm{min}$.
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