High School

Find the area under the standard normal distribution curve to the left of [tex]z = 1.69[/tex]. Write as a percent rounded to the nearest hundredth of a percent.

Answer :

The area under the standard normal distribution curve to the left of z = 1.69, as found using a standard normal distribution table or calculator, is approximately 95.45%. This is the cumulative frequency of all data points up to z = 1.69 in a standard normal distribution.

Explanation:

The area under the standard normal distribution curve to the left of z = 1.69 is representing the cumulative frequency of all the data points up to the z-score of 1.69. This value can be found using standard normal distribution tables or a standard normal distribution calculator. These tools give us the probability of a data point falling below a certain z-score in a normal distribution, which is also the area under the curve to the left of that z-score.

Using a z-table, we find that the area to the left of z = 1.69 is approximately 0.9545, or 95.45%. Therefore, the area under the standard normal distribution curve to the left of z= 1.69 is 95.45%, rounded to the nearest hundredth of a percent.

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