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Answer:
41.64% probability that a butterfly will live between 12.04 and 18.38 days.
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:
Find the probability that a butterfly will live between 12.04 and 18.38 days.
This is the pvalue of Z when X = 18.38 subtracted by the pvalue of Z when X = 12.04. So
X = 18.38
has a pvalue of 0.4168
X = 12.04
has a pvalue of 0.0004
0.4168 - 0.0004 = 0.4164
41.64% probability that a butterfly will live between 12.04 and 18.38 days.