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.

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step-by-step explanation:

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