For a mean of 153 and standard deviation of 25, find P(130leqslant Xleqslant 170) square A.

## Step 1: Calculate the z-scores<br />### To standardize the values 130 and 170, we use the z-score formula: $z = \frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $x = 130$, $z = \frac{130 - 153}{25} = \frac{-23}{25} = -0.92$. For $x = 170$, $z = \frac{170 - 153}{25} = \frac{17}{25} = 0.68$.<br /><br />## Step 2: Find the probabilities corresponding to the z-scores<br />### Using a z-table or calculator, we find the probabilities corresponding to the calculated z-scores. $P(Z \le -0.92) \approx 0.1788$ and $P(Z \le 0.68) \approx 0.7517$.<br /><br />## Step 3: Calculate the probability between the two z-scores<br />### The probability $P(130 \le X \le 170)$ is equivalent to $P(-0.92 \le Z \le 0.68)$. This can be calculated as $P(Z \le 0.68) - P(Z \le -0.92) = 0.7517 - 0.1788 = 0.5729$.