### 7.22 Because \( P(z < 0.44) = 0.67 \), 67% of all \( z \) values are less than 0.44, and 0.44 is the 67th percentile of the standard normal distribution. Determine the value of each of the following percentiles for the standard normal distribution (Hint: If the cumulative area that you must look for does not appear in the \( z \) table, use the closest entry): a. The 91st percentile (Hint: Look for area 0.9100.) b. The 77th percentile c. The 50th percentile d. The 9th percentile e. What is the relationship between the 70th \( z \) percentile and the 30th \( z \) percentile?

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### 7.22

Because \( P(z < 0.44) = 0.67 \), 67% of all \( z \) values are less than 0.44, and 0.44 is the 67th percentile of the standard normal distribution. Determine the value of each of the following percentiles for the standard normal distribution (Hint: If the cumulative area that you must look for does not appear in the \( z \) table, use the closest entry):

a. The 91st percentile (Hint: Look for area 0.9100.)  
b. The 77th percentile  
c. The 50th percentile  
d. The 9th percentile  
e. What is the relationship between the 70th \( z \) percentile and the 30th \( z \) percentile?
Transcribed Image Text:### 7.22 Because \( P(z < 0.44) = 0.67 \), 67% of all \( z \) values are less than 0.44, and 0.44 is the 67th percentile of the standard normal distribution. Determine the value of each of the following percentiles for the standard normal distribution (Hint: If the cumulative area that you must look for does not appear in the \( z \) table, use the closest entry): a. The 91st percentile (Hint: Look for area 0.9100.) b. The 77th percentile c. The 50th percentile d. The 9th percentile e. What is the relationship between the 70th \( z \) percentile and the 30th \( z \) percentile?
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