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

a)

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 and standard deviation , the z-score of a value X is given by:

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, , .

(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 ?

(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 and . 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

Looking at the z score table, we find that the pvlaue of is 0.3859.

When

Looking at the z score table, we find that the pvlaue of 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%

(c) Find the probability that someone scores above a 17 on the Dental Anxiety Scale

This probability is 100% minus the pvalue of the zvalue when

When , 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

i belive those are the ones that are under 90 degreese.

b, i believe, but not sure.