Psychology students at a university completed the Dental Anxiety Scale questionnaire. Scores on the scale range from 0 (no anxiety) to 20 (extreme anxiety). The mean score was 12 and the standard deviation was 3.5. Assume that the distribution of all scores on the Dental Anxiety Scale is normal with u = 12 and o = 3.5. Complete parts a through c. Click here to view a table of areas under the standardized normal curve. a. Suppose you score a 19 on the Dental Anxiety Scale. Find the z-value for this score. z= 2 (Round to the nearest hundredth as needed.) b. Find the probability that someone scores between 11 and 16 on the Dental Anxiety Scale. P(11sxs 16) = 0.4859 (Round to four decimal places as needed.) c. Find the probability that someone scores above 17 on the Dental Anxiety Scale. P(x> 17) =O (Round to four decimal places as needed.)
Psychology students at a university completed the Dental Anxiety Scale questionnaire. Scores on the scale range from 0 (no anxiety) to 20 (extreme anxiety). The mean score was 12 and the standard deviation was 3.5. Assume that the distribution of all scores on the Dental Anxiety Scale is normal with u = 12 and o = 3.5. Complete parts a through c. Click here to view a table of areas under the standardized normal curve. a. Suppose you score a 19 on the Dental Anxiety Scale. Find the z-value for this score. z= 2 (Round to the nearest hundredth as needed.) b. Find the probability that someone scores between 11 and 16 on the Dental Anxiety Scale. P(11sxs 16) = 0.4859 (Round to four decimal places as needed.) c. Find the probability that someone scores above 17 on the Dental Anxiety Scale. P(x> 17) =O (Round to four decimal places as needed.)
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Find the probability that someone scores above 17 on the Dental Anxiety Scale.
P(x>17)=
(Round to four decimal places as needed.)![### Dental Anxiety Scale Analysis
Psychology students at a university completed the Dental Anxiety Scale questionnaire. Scores on the scale range from 0 (no anxiety) to 20 (extreme anxiety). The mean score was 12 and the standard deviation was 3.5. Assume that the distribution of all scores on the Dental Anxiety Scale is normal with mean \(\mu = 12\) and standard deviation \(\sigma = 3.5\). Complete parts a through c.
<a> Click here to view a table of areas under the standardized normal curve. </a>
---
**a. Suppose you score a 19 on the Dental Anxiety Scale. Find the z-value for this score.**
\[ z = \frac{19 - 12}{3.5} = \frac{7}{3.5} = 2 \]
(Round to the nearest hundredth as needed.)
**b. Find the probability that someone scores between 11 and 16 on the Dental Anxiety Scale.**
\[ P(11 \leq x \leq 16) = 0.4859 \]
(Round to four decimal places as needed.)
**c. Find the probability that someone scores above 17 on the Dental Anxiety Scale.**
\[ P(x > 17) = \]
(Round to four decimal places as needed.)
---
### Explanation of Concepts:
1. **Z-Value Calculation:**
- The z-value is a measure of how many standard deviations an element is from the mean. It is calculated using the formula:
\[
z = \frac{X - \mu}{\sigma}
\]
where \( X \) is the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
2. **Probability Calculations:**
- The probability of a score falling within a certain range (e.g., between 11 and 16) or above a certain threshold (e.g., above 17) can be determined using the standard normal distribution table or software tools that provide cumulative distribution functions for normal distributions.
3. **Normal Distribution:**
- In a normal distribution, most values cluster around the mean. The standard deviation measures the spread of the data points. In this context, a score of 19 is relatively high, indicating a higher level of anxiety compared to the average student score, which is 12.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb12ea80c-4b65-4f73-8432-877797ccd5cd%2F878c9463-01cc-482a-9abb-2bb8fb5a8043%2Fn8yvx6k_processed.png&w=3840&q=75)
Transcribed Image Text:### Dental Anxiety Scale Analysis
Psychology students at a university completed the Dental Anxiety Scale questionnaire. Scores on the scale range from 0 (no anxiety) to 20 (extreme anxiety). The mean score was 12 and the standard deviation was 3.5. Assume that the distribution of all scores on the Dental Anxiety Scale is normal with mean \(\mu = 12\) and standard deviation \(\sigma = 3.5\). Complete parts a through c.
<a> Click here to view a table of areas under the standardized normal curve. </a>
---
**a. Suppose you score a 19 on the Dental Anxiety Scale. Find the z-value for this score.**
\[ z = \frac{19 - 12}{3.5} = \frac{7}{3.5} = 2 \]
(Round to the nearest hundredth as needed.)
**b. Find the probability that someone scores between 11 and 16 on the Dental Anxiety Scale.**
\[ P(11 \leq x \leq 16) = 0.4859 \]
(Round to four decimal places as needed.)
**c. Find the probability that someone scores above 17 on the Dental Anxiety Scale.**
\[ P(x > 17) = \]
(Round to four decimal places as needed.)
---
### Explanation of Concepts:
1. **Z-Value Calculation:**
- The z-value is a measure of how many standard deviations an element is from the mean. It is calculated using the formula:
\[
z = \frac{X - \mu}{\sigma}
\]
where \( X \) is the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
2. **Probability Calculations:**
- The probability of a score falling within a certain range (e.g., between 11 and 16) or above a certain threshold (e.g., above 17) can be determined using the standard normal distribution table or software tools that provide cumulative distribution functions for normal distributions.
3. **Normal Distribution:**
- In a normal distribution, most values cluster around the mean. The standard deviation measures the spread of the data points. In this context, a score of 19 is relatively high, indicating a higher level of anxiety compared to the average student score, which is 12.
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