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The figure is

Formula used:$\text{population mean and standard deviation:}{\mathrm{μ}}_{\stackrel{¯}{x}}=\mathrm{μ}\text{and}{\mathrm{σ}}_{\stackrel{¯}{x}}=\mathrm{σ}/\sqrt{n}\text{.}$

Because the population variable in $Fig7.6\left(a\right)$ is regularly distributed, and we know that sample means for normally distributed population variables are always distrusted, $\mathrm{μ}$and $s.d.$, ${\mathrm{σ}}_{\stackrel{¯}{x}}=\frac{\mathrm{σ}}{\sqrt{n}}$

Thus, regardless of sample size, the mean of the sample means is equal to $\mathrm{μ}$As a result, all four graphs in Figure $7.6$(a) for various sample sizes are centered at the same position $\mathrm{μ}$

We know that the sample means S.D. equals $\frac{\mathrm{σ}}{\sqrt{n}}$, i.e. it is inversely proportional to the square root of the sample size $n$As the sample size increases, the S.D. of the sample mean lowers, and the graph's spread shrinks.

We all know that standard deviation is a measure of dispersion; it tells us how far the observations are spread out or departed from the mean value. As a result, a small s.d. denotes a tiny variation from the mean value, implying that observations are strongly concentrated around the mean value.

We calculate the population mean using the sample mean $\stackrel{¯}{x}\&$; the mean of $\stackrel{¯}{x}$ is $\mathrm{μ}$, and the standard deviation is ${\mathrm{σ}}_{\stackrel{¯}{x}}$ If ${\mathrm{σ}}_{\stackrel{¯}{x}}$ drops, then At the mean $\mathrm{μ}$, the values of $\stackrel{¯}{x}$ become more concentrated. As a result, when we try to estimate $\mathrm{μ}$ using $\stackrel{¯}{x}$, we can expect the value of $\stackrel{¯}{x}$ to be from a $\mathrm{μ}$ nearest point, lowering the sampling error.

The curve of a normal distribution is bell-shaped because the sample means $\left(\stackrel{¯}{x}\right)$follow the normal distribution.

The population variables in fig $7.6(\mathrm{b})\&7.6$ (c) do not follow a normal distribution. As a result, for small sample sizes, the sample means do not follow a normal distribution. However, for large samples, the distribution of the sample means can be approximated by the normal distribution using CLT.

As a result, the graphs in Figures 7.6(b) and 7.6(c) are not symmetric and bell-shaped for small sample sizes. The distribution of $\stackrel{¯}{x}$'s tends to normalcy as the sample size grows, which is why the graphs become bell-shaped.