2. the welcher adult intelligence test scale is composed of a number of subtests. on one subtest, the raw scores have a mean of 35 and a standard deviation of 6. assuming these raw scores form a normal distribution: a) what number represents the 65th percentile (what number separates the lower 65% of the distribution)? 37.31 b) what number represents the 90th percentile? 42.71 c) what is the probability of getting a raw score between 28 and 38? 57% d) what is the probability of getting a raw score between 41 and 44? 9

a) 37.31

b) 42.68

c) 57.05% probability of getting a raw score between 28 and 38

d) 9.19% probability of getting a raw score between 41 and 44.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

a) What number represents the 65th percentile (what number separates the lower 65% of the distribution)?

This is X when Z has a pvalue of 0.65. So X when Z = 0.385.

b) What number represents the 90th percentile?

This is X when Z has a pvalue of 0.9. So X when Z = 1.28

c) What is the probability of getting a raw score between 28 and 38?

This is the pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 28. So

X = 38

has a pvalue of 0.6915

X = 28

has a pvalue of 0.1210

0.6915 - 0.1210 = 0.5705

57.05% probability of getting a raw score between 28 and 38

d) What is the probability of getting a raw score between 41 and 44?

This is the pvalue of Z when X = 44 subtracted by the pvalue of Z when X = 41. So

X = 44

has a pvalue of 0.9332

X = 41

has a pvalue of 0.8413

0.9332 - 0.8413 = 0.0919

9.19% probability of getting a raw score between 41 and 44.

ca = ec

cpctc makes it so that corresponding parts of the triangle you proved to be equal are equal, the other options aren't part of the part of the triangles you proved to be equal.

central angle of a triangle has the same measure as its intercepted arc.

step-by-step explanation: