This interactive Z table displays probabilities (areas) under the standard normal distribution curve for specific z-scores. It helps determine the probability of values falling within particular ranges in normally distributed data. Hover over any table value to visualize the corresponding shaded area in the distribution chart along with its exact probability. You can also click on any value to pin it and maintain the shaded area visualization for closer examination.
pnorm(1.84)There are two ways to calculate P(Z < z) for negative z-scores:
Let's use the symmetry property for this example:
1 - pnorm(1.25)
# or
pnorm(-1.25)Pro Tip:
Confidence intervals use critical z-scores to determine the range of values that likely contains the true population parameter. Here are the most commonly used confidence levels and their corresponding z-scores:
For any confidence level, the critical z-score corresponds to the point where the cumulative probability equals (1 + confidence level) / 2.
qnorm(0.975) # Returns 1.96qnorm(0.95) # Returns 1.645qnorm(0.995) # Returns 2.576Once you have the critical z-score, use this formula to calculate the confidence interval:
CI = x̄ ± (z × σ/√n)
Where:
- x̄ = sample mean
- z = critical z-score
- σ = population standard deviation
- n = sample sizeA z-score (also called a standard score) measures how many standard deviations an observation is from the mean. The formula is:
z = (x - μ) / σTo calculate a z-score, you need the value (x), population mean (μ), and standard deviation (σ).
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
This interactive Z table displays probabilities (areas) under the standard normal distribution curve for specific z-scores. It helps determine the probability of values falling within particular ranges in normally distributed data. Hover over any table value to visualize the corresponding shaded area in the distribution chart along with its exact probability. You can also click on any value to pin it and maintain the shaded area visualization for closer examination.
pnorm(1.84)There are two ways to calculate P(Z < z) for negative z-scores:
Let's use the symmetry property for this example:
1 - pnorm(1.25)
# or
pnorm(-1.25)Pro Tip:
Confidence intervals use critical z-scores to determine the range of values that likely contains the true population parameter. Here are the most commonly used confidence levels and their corresponding z-scores:
For any confidence level, the critical z-score corresponds to the point where the cumulative probability equals (1 + confidence level) / 2.
qnorm(0.975) # Returns 1.96qnorm(0.95) # Returns 1.645qnorm(0.995) # Returns 2.576Once you have the critical z-score, use this formula to calculate the confidence interval:
CI = x̄ ± (z × σ/√n)
Where:
- x̄ = sample mean
- z = critical z-score
- σ = population standard deviation
- n = sample sizeA z-score (also called a standard score) measures how many standard deviations an observation is from the mean. The formula is:
z = (x - μ) / σTo calculate a z-score, you need the value (x), population mean (μ), and standard deviation (σ).
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.