Question

Eruptions of Old Faithful have duration times with a mean of 245.0 sec and a standard deviation of 36.4 sec. One eruption had a duration time of 110 sec. is the duration time of 110 sec unusual?

Answer 1

Solution:
Given in the question
Eruptions of Old Faithful have duration times with a
Mean () = 245
Standard deviation() = 36.4
One eruption had a duration time of 110 sec
To calculate "is the duration time of 110 sec unusual?", we will use the normal distribution, first we will calculate Z-score which can be calculated as
Z-score = (X-)/ = (110 - 245)/36.4 = -135/36.4 = -3.71
A score considered Unusual if Z-score is greater than 2 or less than -2. Here we can see that Z-score is less than -2. i.e. (-3.71<-2). So we can say that the duration time of 110 sec unusual.