find the value of normal distribution with a 3 decimal places Z score using table

Question

In a past exam of my stats class, the question requires finding the value of a normal CDF corresponding to a Z score of 3 DP. However, we are only given a table that is accurate to 2 DP. We are not allowed to use calculator. What should I do to find the value when the Z score is 1.293, not just 1.29.

Answer 1

Personally, I would just round to $1.29$. However, if you really want to guess $\text{normalcdf}(1.293)$, I would just do a weighted sum.

First, write $1.293$ in terms of $1.29$ and $1.30$, since those are the two-decimal z-scores closest to it:

$$1.293=0.7\cdot 1.29+0.3\cdot 1.30$$

Then, pretend $\text{normalcdf}$ is linear:

$$\text{normalcdf}(1.293)=0.7\text{normalcdf}(1.29)+0.3\text{normalcdf}(1.30) \\ =0.7\cdot 0.9015+0.3\cdot 0.9032=0.90201$$