Mathematics, 19.09.2019 19:30 ghst

Psychology students at wittenberg university completed the dental anxiety scale questionnaire (psychological reports, august 1997). scores on the scale range from 0 (no anxiety) to 20 (extreme anxiety). the mean score was 11 and the standard deviation was 3.5. assume that the distribution of all scores on the dental anxiety scale is normal with μ = 11 and σ = 3.5. (a) suppose you score a 16 on the dental anxiety scale. find the z-value for this score. (b) find the probability that someone scores between a 10 and a 15 on the dental anxiety scale. (c) find the probability that someone scores above a 17 on the dental anxiety scale

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Answer from: 21ghostrider21

a) Z = 1.43

b) There is a 48.696% probability that someone scores between a 10 and a 15 on the Dental Anxiety Scale is

Step-by-step explanation:

Normal model problems can be solved by the zscore formula.

On a normaly distributed set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a value X is given by:

$Z = \frac{X - \mu}{\sigma}$

Each z-score value has an equivalent p-value, that represents the percentile that the value X is.

In our problem, the mean score was 11 and the standard deviation was 3.5.

So, $\mu = 11$ , $\sigma = 3.5$ .

(a) Suppose you score a 16 on the Dental Anxiety Scale. Find the z-value for this score.

What is the value of Z when X = 16 ?

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{16 - 11}{3.5} = 1.43$

(b) Find the probability that someone scores between a 10 and a 15 on the Dental Anxiety Scale.

We have to find the percentiles of both of these scores. This means that we have to find Z when X = 10 and X = 15 . The probability that someone scores between a 10 and a 15 is the difference between the pvalues of the z-value of X = 10 and X = 15.

When X = 10

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{10 - 11}{3.5} = -0.29$

Looking at the z score table, we find that the pvlaue of Z = -0.29 is 0.3859.

When X = 15

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{15 - 11}{3.5} = 1.14$

Looking at the z score table, we find that the pvlaue of Z = 1.14 is 0.87286.

So, the probability that someone scores between a 10 and a 15 on the Dental Anxiety Scale is

0.87286 - 0.3859 = 0.48696 = 48.696%

This probability is 100% minus the pvalue of the zvalue when X = 17

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{17 - 11}{3.5} = 1.71$

When Z = 1.71 , the pvalue is 0.95637. This means that there is a 95.637% probability that someone scores BELOW 17 on the dental anxiente scale.

100 - 95.637 = 4.363%

There is 4.363% probability that someone scores above a 17 on the Dental Anxiety Scale

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