91影视

The meanweights of seeds, $\overline{x}=525mg$

The standard deviation, $s=110mg$

Biological measurements of the same species are considered to frequently follow a Normal distribution.

A simple random sample (SRS) of size $n$ is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

It is given in the question that,

$$\begin{gathered} 渭=525 \\ 蟽=110 \\ x=500 \end{gathered}$$

The $z-$score is calculated as follows:

$$\begin{gathered} z=\frac{x鈭�渭}{蟽} \\ =\frac{500鈭�525}{110} \\ =\frac{鈭�25}{110} \\ =鈭�0.23 \end{gathered}$$

Thus the probability can be calculated as:

$$\begin{gathered} P(X<500)=P(Z<鈭�0.23) \\ =0.4090 \end{gathered}$$

As a result of using the complement rule, we now have

$$\begin{gathered} P(X>500)=1鈭�P(X<500) \\ =1鈭�0.4090 \\ =0.5910 \\ =59.10\% \end{gathered}$$

It is stated in the question, $$\begin{gathered} 渭=525 \\ 蟽=110 \end{gathered}$$

To begin, get the$z-$score in table A that corresponds to a $10\%$ likelihood as follows:

$z=鈭�1.28$

Then the $z-$score will be as:

$z=\frac{x鈭�渭}{蟽}$

Thus, by evaluating it we get,$$\begin{gathered} z=\frac{x鈭�渭}{蟽} \\ 鈬�z蟽=x鈭�渭 \\ 鈬�渭+z蟽=x \end{gathered}$$

As a result of solving this equation for the unknown value: $$\begin{gathered} x=渭+z蟽 \\ =525鈭�1.28\left(110\right) \\ =384.2 \end{gathered}$$

After discarding the lightest $10\%$ of the seeds, we know that the smallest weight among the remaining seeds is $384.2$ milligrams.