Answer:
a) 8.2962
b) 6.3956
c) 3.845
Step-by-step explanation:
Z-score:
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 question, we have that:
(a) What response represents the 85th percentile?
This is X when Z has a pvalue of 0.85. So X when Z = 1.037.
(b) What response represents the 62nd percentile?
This is X when Z has a pvalue of 0.62. So X when Z = 0.306.
(c) What response represents the first quartile?
The first quartile is the 100/4 = 25th percentile. So this is X when Z has a pvalue of 0.25, so X when Z = -0.675.