Final answer:
To calculate the probability that z is greater than -1.82, one must first use the z-table to find the area to the left of -1.82. Then, subtract this area from 1 to get the area to the right, which gives us the desired probability.
Step-by-step explanation:
To find the probability that the standard normal variable z is greater than -1.82, we use the properties of the standard normal distribution and a z-table or a statistical calculator.
Step-by-Step Solution:
- Identify the given z-score: In this case, z = -1.82.
- Use a z-table or statistical calculator to determine the area to the left of z = -1.82. For most z-tables, this value must be looked up directly under the z-column.
- The z-table typically provides the area to the left of the given z-score. Since we want the probability that z is greater than -1.82, we need to find the area to the right. If the z-table shows the area to the left is 0.6554, we subtract this from 1 to get the area to the right. The formula for this calculation is P(z > -1.82) = 1 - P(z < -1.82).
- The final probability is given by 1 - 0.6554 = 0.3446.
If using a statistical calculator such as a TI-83, 83+, or 84+, you can use the command inform (0.6554,0,1) to get the z-score directly.
To find P(x > 65), you would need to convert the raw score (x) to a z-score using the mean and standard deviation of the distribution. The z-score formula is z = (x - mean) / standard deviation. Once you have the z-score, you can use the same process as above to find the corresponding probability.