Final answer:
Using the z-table, calculated that the value of z is approximately 1.04.
Step-by-step explanation:
To find z such that 69% of the standard normal curve lies between -x and z, we first understand that the standard normal distribution is symmetrical around the mean.
Since 69% is close to the empirical rule's 68%, we might expect z to be close to 1.
However, because we are looking for a precise value and not using the empirical rule, we need to adjust this estimate.
First, we know that if 69% of the area is between -x and z, then the area to the left of z is 0.345 (half of 69%) plus 0.5 (the left half of the distribution), giving a total of 0.845 of the area under the curve.
By using a z-table or a standard normal distribution calculator, we find the z-score that corresponds with an area to the left of 0.845.
The z-table generally provides the area to the left of a z-score.
Looking this up, we find that z is approximately 1.04.
So z = 1.04 (rounded to two decimal places).