Answer:
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