Answer:
a) 73.02% of vehicle speeds were between 27 and 57 mph
b) 19.77% of vehicle speeds exceeded 57 mph
Step-by-step explanation:
Problems of normally distributed distributions 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 question, we have that:
A. Roughly what proportion of vehicle speeds were between 27 and 57 mph?
This is the pvalue of Z when X = 57 subtracted by the pvalue of Z when X = 27. So
X = 57
has a pvalue of 0.8023.
X = 27
has a pvalue of 0.0721
0.8023 - 0.0721 = 0.7302
73.02% of vehicle speeds were between 27 and 57 mph
B. Roughly what proportion of vehicle speeds exceeded 57 mph?
This is 1 subtracted by the pvalue of Z when X = 57.
From a), when X = 57, Z = 0.85, which has a pvalue of 0.8023.
1 - 0.8023 = 0.1977
19.77% of vehicle speeds exceeded 57 mph
