Answer: Assuming a standard normal distribution, we know that the total area under the curve is equal to 1. Since 0.8904 of the area lies between -z and z, the remaining area (0.1096) lies outside of this range.
Since the normal distribution is symmetric around the mean, the area to the left of -z is the same as the area to the right of z. Therefore, we can find the area to the right of z by subtracting 0.1096 from 1 and dividing by 2:
(1 - 0.1096)/2 = 0.4452
We can use a standard normal distribution table or calculator to find the z-score that corresponds to an area of 0.4452 to the right of the mean. This z-score is approximately 1.70.
Therefore, the value of z such that 0.8904 of the area lies between -z and z is approximately 1.70. Rounded to two decimal places, this is 1.70.
Explanation: