Answer:
a,b) x represents the general attitude of these students toward recreational reading.
c) The 10th percentile of sample means is 102.51.
d)
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
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 This p-value is the probability that the value of the measure is greater than X.
In this case, we have that:
The mean score for this population of children was 106 points, with a standard deviation of 16.4 points, so .
a,b) What is x?
x represent the mean recreational reading attitude score for the sample. So x represents the general attitude of these students toward recreational reading.
c) What sample mean would be the cutoff for the bottom 10% of sample means. (You are being asked for the 10th percentile of sample means.)
This is the value of X when Z has a pvalue of 0.10.
Looking at the Z table, that is .
We are working with the mean of the sample, so we have to find the standard deviation of the sample. That is
The 10th percentile of sample means is 102.51.
d) Find P(x < 100).
This is the pvalue of Z when X = 100.
has a pvalue of 0.01390.
So .