Find the indicated probability using the standard normal distribution.
\[
P(-1.42< z< 0)
\]
Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table.
$P(-1.42< z< 0)=$
(Round to four decimal places as needed.)
Answer
Final Answer: The probability that z is between -1.42 and 0 is approximately \(\boxed{0.4222}\).
Step 1 ：The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The variable z represents the number of standard deviations from the mean.
Step 2 ：The probability that z is between -1.42 and 0 can be found by looking up the z-scores in the standard normal table and subtracting the probabilities.
Step 3 ：The probability of z being less than 0 is 0.5 (since the standard normal distribution is symmetric about the mean).
Step 4 ：The probability of z being less than -1.42 can be found from the standard normal table, which is approximately 0.0778.
Step 5 ：Subtract the probability of z being less than -1.42 from the probability of z being less than 0 to find the probability that z is between -1.42 and 0: \(0.5 - 0.0778 = 0.4222\).
Step 6 ：Final Answer: The probability that z is between -1.42 and 0 is approximately \(\boxed{0.4222}\).
