Let $\mathrm{x}$ be a continuous random variable with a standard normal distribution. Using the accompanying standard normal distribution table, find $P(-1.74\le x\le 0)$.
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$P(-1.74\le x\le 0)=◻($ Round to four decimal places as needed. $)$

Step 1 ：Let $x$ be a continuous random variable with a standard normal distribution. We are asked to find $P(-1.74\le x\le 0)$.

Step 2 ：The standard normal distribution table gives the probability that a standard normal random variable is less than a given value. In other words, it gives the cumulative distribution function (CDF) for a standard normal random variable.

Step 3 ：To find $P(-1.74\le x\le 0)$, we need to find the CDF at 0 and at -1.74, and subtract the two.

Step 4 ：The CDF at 0 is 0.5 (since the standard normal distribution is symmetric about 0), and the CDF at -1.74 can be found from the table.

Step 5 ：Using the given values, we have cdf_0 = 0.5 and cdf_minus_174 = 0.0409.

Step 6 ：Subtracting these values, we get p = 0.4591.

Step 7 ：Thus, the final answer is $P(-1.74\le x\le 0)=\boxed{{\displaystyle 0.4591}}$ (rounded to four decimal places).