Find the indicated probability using the standard normal distribution.
\[
P(z< -2.58)
\]
- Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table.
$P(z< -2.58)=\square($ Round to four decimal places as needed. $)$
Answer
Final Answer: The probability that a value from a standard normal distribution is less than -2.58 is approximately \(\boxed{0.0049}\).
Step 1 ：The problem is asking for the probability that a value from a standard normal distribution is less than -2.58. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The z-score of -2.58 means that the value is 2.58 standard deviations below the mean.
Step 2 ：To find this probability, we can use the cumulative distribution function (CDF) for a standard normal distribution. The CDF gives the probability that a random variable is less than or equal to a certain value.
Step 3 ：Using the CDF, we find that the probability that a value from a standard normal distribution is less than -2.58 is approximately 0.0049. This means that about 0.49% of the values from a standard normal distribution are less than -2.58.
Step 4 ：Final Answer: The probability that a value from a standard normal distribution is less than -2.58 is approximately \(\boxed{0.0049}\).
