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A company manufactures 2,000 units of its flagship product in a day. The quality control department takes a random sample of 40 units to test for quality. The product is put through a wear-and-tear test to determine the number of days it can last. If the product has a lifespan of less than 26 days, it is considered defective. The table gives the sample data that a quality control manager collected.

\begin{tabular}{|l|l|l|l|l|}
\hline 39 & 31 & 38 & 40 & 29 \\
\hline 32 & 33 & 39 & 35 & 32 \\
\hline 32 & 27 & 30 & 31 & 27 \\
\hline 30 & 29 & 34 & 36 & 25 \\
\hline 30 & 32 & 38 & 35 & 40 \\
\hline 29 & 32 & 31 & 26 & 26 \\
\hline 32 & 26 & 30 & 40 & 32 \\
\hline 39 & 37 & 25 & 29 & 34 \\
\hline
\end{tabular}

The point estimate of the population mean is [tex]$\square$[/tex]. The point estimate of the proportion of defective units is [tex]$\square$[/tex].



Answer :

GinnyAnswer
To determine the point estimate of the population mean lifespan of the product, we use the sample data provided. The population mean is estimated by calculating the average (mean) of the sample data.

Given the sample data:
[tex]\[ \begin{aligned} &39, 31, 38, 40, 29 \\ &32, 33, 39, 35, 32 \\ &32, 27, 30, 31, 27 \\ &30, 29, 34, 36, 25 \\ &30, 32, 38, 35, 40 \\ &29, 32, 31, 26, 26 \\ &32, 26, 30, 40, 32 \\ &39, 37, 25, 29, 34 \\ \end{aligned} \][/tex]

The point estimate of the proportion of defective units is determined by counting the number of units in the sample that are considered defective (i.e., with a lifespan of less than 26 days) and dividing it by the total number of units in the sample.

The calculated values are as follows:
- The point estimate of the population mean is [tex]\( 32.3 \)[/tex].
- The point estimate of the proportion of defective units is [tex]\( 0.05 \)[/tex].

So, the point estimate of the population mean is [tex]\( 32.3 \)[/tex], and the point estimate of the proportion of defective units is [tex]\( 0.05 \)[/tex].

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