1) psychology students at wittenberg university completed the dental anxiety scale questionnaire. 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 with \mu = 11 and \sigma = 3.5.
a) find the probability that someone scores between a 10 and a 15 on the dental anxiety scale.
b) find the probability that someone scores above a 17 on the dental anxiety scale.
2) ecological applications published a study on the development of forests following wildfires in the pacific northwest. one variable of interest to the researcher was tree diameter at breast height 110 years after the fire. the population of douglas fir trees was shown to have an approximately normal diameter distribution, with \mu = 50 centimeters and \sigma = 12 cm. find the diameter, d, such that 30% of the douglas fir trees in the population have diameters that exceed d.

1) 0.487,0.0436

2) 56.3 cm

Step-by-step explanation:

Let X be the scores ranging from 0 to 20 of the  Psychology students at Wittenberg University completed the Dental Anxiety Scale questionnaire.

X is N(11,3.5)

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

=

b)

c) Y is N(50, 20) where Y is tree diameter at breast height 110 years after the fire.

P(X>d) = 0.30

Corresponding Z value = 0.525

d = 56.3 cm

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.

answer: bea's uncle is 25 years old.

step-by-step explanation:

given the equation , we can say that the variable "x" represents the age of bea's uncle. then to find his age, we need to solve for "x":

we must add 15 to both sides of the equation:

now we need to divide both sides of the equation by 3:

therefore, we can conclude that bea's uncle is 25 years old.