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Answer:
38.46% probability that the sample proportion will NOT be between 0.60 and 0.73
Step-by-step explanation:
Problems of normally distributed samples are 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.
For a proportion p in a sample of size n, we have that
In this problem, we have that:
So
What is the probability that the sample proportion will NOT be between 0.60 and 0.73?
This is 1 subtracted by the probability that it is between 0.6 and 0.73.
Probability it is between 0.6 and 0.73
pvalue of Z when X = 0.73 subtracted by the pvalue of Z when X = 0.6. So
X = 0.73
has a pvalue of 0.6772
X = 0.6
has a pvalue of 0.0618
0.6772 - 0.0618 = 0.6154
NOT be between 0.60 and 0.73?
1 - 0.6154 = 0.3846
38.46% probability that the sample proportion will NOT be between 0.60 and 0.73