<h1 style="box-sizing: border-box; margin: 0px; font-weight: 500; line-height: 1.5; font-size: 2.4em; font-family: Poppins, sans-serif; color: var(--iq-title-text); letter-spacing: 1px; background-color: #ffffff;">Using a Z Table to Determine Probabilities</h1>
<p><img style="box-sizing: border-box; vertical-align: middle; border-style: none; max-width: 38%; color: #585858; font-family: Poppins, sans-serif; letter-spacing: 1px; background-color: #ffffff; max-height: 365px; height: auto; margin: 0px 10px; width: auto;" src="https://i.imgur.com/jbbVc50.jpg" alt="z table" align="right" /></p>
<p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 1rem; color: #585858; font-family: Poppins, sans-serif; letter-spacing: 1px; background-color: #ffffff;">Using a Z table can be a useful tool in determining probabilities. A Z-score is used to compare two sets of data that have different means and standard deviations. It is important to understand the various types of Z-scores and how they can be used.</p>
<p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 1rem; color: #585858; font-family: Poppins, sans-serif; letter-spacing: 1px; background-color: #ffffff;">A positive z-score is used to describe values that are above the mean. A negative z-score is used to describe those values that are below the mean. The value for a -1.0 z-score is 0.1587, while the value for a -0.23 z-score is 0.01287. The area to the left of a z-score is calculated by subtracting the value from the table. The table can also be used to determine probability of a specific statistic.</p>
<p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 1rem; color: #585858; font-family: Poppins, sans-serif; letter-spacing: 1px; background-color: #ffffff;">The probabilities for a specific statistic can be found by integrating the probability density function. The integral of a probability density function gives the area below the lowest and the highest values. The table also contains the probability of a variable falling within a range. Adding or subtracting the areas under the curve can give other probabilities.</p>
<p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 1rem; color: #585858; font-family: Poppins, sans-serif; letter-spacing: 1px; background-color: #ffffff;">To use a z-table, you must first convert your data into a standard normal distribution. The z-table is then used to determine the percentage of the data that falls below or above a z-score. The z-score can then be compared with the probability of a random variable lying between the standard normal distribution.</p>
<p style="box-sizing: border-box; margin-top: 0px; margin-bottom: 1rem; color: #585858; font-family: Poppins, sans-serif; letter-spacing: 1px; background-color: #ffffff;">The z-table is useful in finding the probability of certain outcomes within an interval. It can be used to find probabilities of p-values, percentiles, and probability of a random variable falling between the standard normal distribution. It can also be used to determine the area of a normal distribution curve.</p>