Let $\mathrm{x}$ be a continuous random variable with a standard normal distribution. Using the accompanying standard normal distribution table, find $P(-1.74 \leq x \leq 0)$.
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$P(-1.74 \leq x \leq 0)=\square($ 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 \(P(-1.74 \leq x \leq 0)\).

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 \(P(-1.74 \leq x \leq 0)\), 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 \(P(-1.74 \leq x \leq 0) = \boxed{0.4591}\) (rounded to four decimal places).