Answer:
35% of all sample proportions be will be above 0.6074.
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:
Of the 1,300 children participating in a town's parks and recreations programs, 765 are under the age of 8. This means that
In the sampling distribution of sample proportions of size 100, above what proportion will 35% of all sample proportions be?
We are using sample proportions of size 100, so
.
In the sampling distribution of sample proportions of size 100, above what proportion will 35% of all sample proportions be?
This proportion is the value of X in the 65th percentile, that is, when Z has a pvalue of 0.65. This is . So
35% of all sample proportions be will be above 0.6074.