Find the area under the normal distribution curve to the left of z = 2.35.
To find the area under the normal distribution curve to the left of z = 2.35, you need to use a standard normal distribution table or a calculator.
If you're using a standard normal distribution table, look for the corresponding value for 2.35. The probability associated with this value represents the area to the left of z = 2.35. Keep in mind that the table typically provides values for z-scores rounded to two decimal places. So, you may need to use the closest value available in the table.
If you're using a calculator, you can use the cumulative distribution function (CDF) for the standard normal distribution. This function will give you the area to the left of a given z-score. For z = 2.35, you can use the CDF function to find the area under the normal distribution curve to the left of this value.
Let me know if you would like assistance with either the table lookup or the calculator method.
To find the area under the normal distribution curve to the left of z = 2.35, we need to use a standard normal distribution table or calculator.
1. Standardize the z-value: To use the standard normal distribution table, we need to convert the z-value to its corresponding value on the standard normal distribution. Since the standard normal distribution has a mean of 0 and a standard deviation of 1, we can standardize z = 2.35 using the formula:
standardized_z = (z - mean) / standard_deviation
In this case, mean = 0 and standard_deviation = 1, so the calculation becomes:
standardized_z = (2.35 - 0) / 1 = 2.35
2. Look up the area in the standard normal distribution table: Use the standardized_z value from step 1 to find the area under the standard normal curve to the left of z = 2.35. Standard normal distribution tables provide the area to the left of a given z-value.
Using the table or a calculator, you should find that the area to the left of z = 2.35 is approximately 0.9906.
Therefore, the area under the normal distribution curve to the left of z = 2.35 is approximately 0.9906.