For a standard normal distribution, find: P(-0.72 < z < 0.38)

Answer 1

Hi Abby,

Assuming you do not have access to a TI-84 Calculator:

1. Use a z-score table.
2. If you do not have one, look one up online.
3. Looking over the "Negative Z-Score Table," you should find the area (to the left) for a z-score of (-)0.72.
4. It should be 0.23576.
5. Looking over the "Positive Z-Score Table," you should find the area (to the left) for a z-score of (+)0.38.
6. It should be 0.64803.
7. Calculate the area (or probability) in between the two z-scores.
8. There are different ways to do this, but I think the simplest way is by subtracting both areas (probabilities found).
9. The probability of a z-score (+)0.38 minus the probability of a z-score (-)0.72.
10. 0.64803 - 0.25576 = 0.41227
11. Round the final answer to four decimal places.
12. 0.4123

Assuming you have access to a TI-84 Calculator:

1. Determine which calculator function to use.
2. Since we need to find the probability (or area) from a standard normal distribution, we will use the "normalcdf(..)" function.
3. Note: If instead we wanted to find an x-value or a z-score, we will use "invNorm(..)"
4. Determine what values to input.
5. Lower: -0.72
6. The lower bound of this probability distribution is the lowest/minimum value.
7. Upper: 0.38
8. The upper bound of this probability distribution is the highest/maximum value.
9. Mean: 0
10. Understanding the properties of a standard normal distribution helps us. For a standard normal distribution, the mean will be zero.
11. Standard Deviation: 1
12. Understanding the properties of a standard normal distribution helps us. For a standard normal distribution, the standard deviation will be one.
13. Round the final answer to four decimal places (based on rounding rules for probabilities).
14. 0.4123