How would I solve this Percentile equation step by step?

Question

Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P₃₅, the 35-percentile. This is the temperature reading separating the bottom 35% from the top 65%.

Answer 1

Since the distribution is Normal, the probability values found on the z-table will double as percentile. For example, a z-value of 0 has P(z<0) = 0.50 = 50%. This means a z-value of 0 is the 50th percentile.

So, look at your z-table and find the z-value (or the one closest to it) that gives a probability of 0.35 = 35%. You will find something like z = -0.39 will give .3483. Depending on instructions you may have to use z=-0.38 or even z=-0.385 (halfway in between the previous two values) because you won't get an exact value.

Next, you go to your z-score formula z=(x-μ)/σ and plug in the values you know and solve for x.