Determine the probability that z falls between -2.69 and 0:
$P(-2.69< z< 0)=$
Answer
Final Answer: The probability that a standard normal random variable z falls between -2.69 and 0 is approximately \(\boxed{0.496}\).
Step 1 ：The problem is asking for the probability that a standard normal random variable z falls between -2.69 and 0. The standard normal distribution has a mean of 0 and a standard deviation of 1. The probability that z falls between -2.69 and 0 is the area under the standard normal curve between these two values.
Step 2 ：To calculate this, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF at a certain point x gives the probability that a standard normal random variable is less than or equal to x. Therefore, to find the probability that z is between -2.69 and 0, we can calculate the CDF at 0 and subtract the CDF at -2.69.
Step 3 ：Using the standard normal distribution table, we find that the CDF at 0 is 0.5 and the CDF at -2.69 is approximately 0.00357.
Step 4 ：Subtracting the CDF at -2.69 from the CDF at 0 gives us the probability that z falls between -2.69 and 0. So, \(0.5 - 0.00357 = 0.49643\).
Step 5 ：Final Answer: The probability that a standard normal random variable z falls between -2.69 and 0 is approximately \(\boxed{0.496}\).
