The lengths of adult males' hands are normally distributed with mean 194 mm and standard deviation is 7.1 mm. Suppose that 7 individuals are randomly chosen. Round all answers to 4 where possible.
The lengths of adult males' hands are normally distributed with mean 194 mm and standard deviation is 7.1 mm. Suppose that 7 individuals are randomly chosen. Round all answers to 4 where possible.
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![## Sample Problem on Adult Males' Hand Lengths
The lengths of adult males' hands are normally distributed with a mean of 194 mm and a standard deviation of 7.1 mm. Suppose that 7 individuals are randomly chosen. Round all answers to 4 decimal places where possible.
### Questions
a. What is the distribution of \(\bar{x}\)?
\[
\bar{x} \sim N(\_\_\_\_\_, \_\_\_\_\_)
\]
b. For the group of 7, find the probability that the average hand length is more than 198.
\[
P(\bar{x} > 198) = \_\_\_\_\_
\]
c. Find the first quartile for the average adult male hand length for this sample size. Round to 2 decimal places.
\[
Q_1 = \_\_\_\_\_
\]
### Explanation of the Diagrams
The visually represented part of this illustration shows numerical results encased within a combination of rounded rectangles and text fields, indicating areas where you will input values. These forms emphasize the structure required for statistical notation and underscore the incorporation of given data in solving probability-oriented problems.
**Note**: The lower portion of the image is obscured behind a striped sheet, obstructing part of the instructions and answers input area.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadb58edc-76a8-4215-8abd-8e37e0700ca4%2F74226998-92f1-40b5-a9b0-27484f9bd0e9%2Fhtwlao.jpeg&w=3840&q=75)
Transcribed Image Text:## Sample Problem on Adult Males' Hand Lengths
The lengths of adult males' hands are normally distributed with a mean of 194 mm and a standard deviation of 7.1 mm. Suppose that 7 individuals are randomly chosen. Round all answers to 4 decimal places where possible.
### Questions
a. What is the distribution of \(\bar{x}\)?
\[
\bar{x} \sim N(\_\_\_\_\_, \_\_\_\_\_)
\]
b. For the group of 7, find the probability that the average hand length is more than 198.
\[
P(\bar{x} > 198) = \_\_\_\_\_
\]
c. Find the first quartile for the average adult male hand length for this sample size. Round to 2 decimal places.
\[
Q_1 = \_\_\_\_\_
\]
### Explanation of the Diagrams
The visually represented part of this illustration shows numerical results encased within a combination of rounded rectangles and text fields, indicating areas where you will input values. These forms emphasize the structure required for statistical notation and underscore the incorporation of given data in solving probability-oriented problems.
**Note**: The lower portion of the image is obscured behind a striped sheet, obstructing part of the instructions and answers input area.
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