I am asked to find the z-score of the proportion .05 to +∞
I look the z-table to find the associated z-score with the value .05. This part I understand I found it to be: -1.64 but then what's the part about +∞ I don't understand what this means or how I am to apply it once I find the associated z-score.
Another problem is similar it asks to find the associated z-score with p=.33 to -∞
I found the z-score to be z=-0.44 but then again where does the -∞ factor into all this?
Thank you
A z-score is a single value: It seems you are being asked to find probabilities based on z-scores, assuming a standard normal distribution.
The number $c$ on the z-scale such that $P(Z > c) = 0.05 = 5\%.$ is $c = 1.645.$ That is, $P(1.645 < Z < \infty) = P(Z > 1.645) = 0.05,$ where $Z$ is a random variable with the standard normal distribution.
Also, $P(Z < -1.645) = 0.05$ and $P(-1.645 < Z < 1.645) = 0.90.$
The figure below shows the standard normal density curve. The total area beneath a density cure is $1$ or 100%. In each 'tail' of the distribution, outside the vertical red lines, there is area 5% representing probability $0.05.$ Between the two red lines there is probability $0.9.$
By contrast, $P(-2.576 < Z < \infty) = 1 - P(Z < -2.576) = 1 - .005 = .995.$ The area to the right of the vertical orange line is 99.5%. The tiny area to the left of the line is $\frac 1 2 \% = 0.005.$
Finally, the number $a$ such that $P(a < Z < \infty) = P(Z > a) = 0.33,$ is $a = 0.4399.$
In the figure below 33% of the probability under the curve lies to the right of the purple line and 67% lies to the left of it.
Notes: (a) In all of these computations the z-values (such as $a, c$) are found in the margins of a printed table of standard normal probabilities, and the probabilities (such as $.0500, 0.0050, and 0.570$) are found in the body of the table. (b) There must be some examples explaining how to use printed standard normal tables in your textbook. Please go through those examples carefully--along with the ones I have provided above. (c) You can't make curves as accurate as mine by hand, but in working problems on normal probabilities, it is a good idea to make a rough sketch of the normal curve, shading in the area that matches the desired probability. That can keep you from getting confused and making huge errors.