91Ó°ÊÓ

MINITAB is used to create the normal probability plot.

Procedure for MINITAB:

Step 1: Select Probability Plot from the Graph menu.

Step 2: Click OK after selecting Single.

Step 3: In the Graph variables section, add the Length column.

Step 4: Click the OK button.

MINITAB OUTPUT:

All observations are closer to a straight line on the probability plot of length. As a result, it may be argued that the length distribution is approximately normal.

Because the data are quite close to a straight line, it is plausible to assume that the carapace length of mature male Brazilian huge tawny red tarantulas is regularly distributed.

Find the $95\%$confidence interval for all adult male Brazilian giant tawny red tarantulas' mean carapace length.

The sample means is$18.43\mathrm{mm}$according to a normal probability plot.

The population standard deviation is $1.76\mathrm{mm}$according to the data.

Empirical rule:

Property 1: Around $68\%$the data set is located between $(\stackrel{¯}{x}-s,\stackrel{¯}{x}+s)$

Property 2: Approximately $95\%$the data set is located between $(\stackrel{¯}{x}-2s,\stackrel{¯}{x}+2s)$

Property 3: Approximately $99.7\%$the data set is located between $(\stackrel{¯}{x}-3s,\stackrel{¯}{x}+3s)$

Using Property $2$, $95\%$all observations fall within two standard deviations of the mean on either side.

The $95\%$confidence interval for the population mean is,

$$\begin{gathered} \stackrel{¯}{x}Â\pm 2\frac{\mathrm{σ}}{\sqrt{n}}=18.43Â\pm 2\left(\frac{1.76}{\sqrt{15}}\right) \\ =18.43Â\pm 0.91 \\ =(18.43-0.91,18.43+0.91) \\ =(17.52,19.34) \end{gathered}$$

The $95\%$ confidence interval for the mean carapace length of all adult male Brazilian huge tawny red tarantulas is thus $(17.52,19.34)$

The mean carapace length of all mature male Brazilian huge tawny red tarantulas is $18.14\mathrm{mm}$ according to Exercise $6.7$ This price ranges from $17.52$ to $19.34$

Yes, the population mean is included in the confidence interval in section (c). This happens around$5\%$ of the time.