Answer:
The standard deviation is $26.67.
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.
In this problem, we have that:
Assuming a normal distribution, if 70 percent of the filings cost less than $171.00, what is the standard deviation?
This means that when X = 171, Z has a pvalue of 0.7. So when Z = 0.525.
The standard deviation is $26.67.