Final answer:
The probability that the standard normal variable Z is between 0 and 0.87 is found using a Z-table or calculator command, resulting in approximately 30.78%.
Step-by-step explanation:
The standard normal distribution Z~N(0,1) describes a normal distribution with a mean of 0 and a standard deviation of 1. To calculate P(0≤Z≤0.87), which is the probability that the value of Z is between 0 and 0.87, one can use a standard normal probability table or a calculator command such as invNorm. Using either of these tools will reveal that P(0≤Z≤0.87) is approximately 0.3078, which means there's a 30.78% chance that Z falls in this range.
For example, if you're using a Z-table, you would look up the value 0.87 in the table to find the area to the left of Z, which should be around 0.8078. Since we're looking for the area from 0, which is the mean, we subtract 0.5 (the total area to the left of the mean) from this value to obtain P(0≤Z≤0.87) = 0.8078 - 0.5 = 0.3078.