Answer:
A task time of 177.125s qualify individuals for such training.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by
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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
In this problem, we have that:
A distribution that can be approximated by a normal distribution with a mean value of 145 sec and a standard deviation of 25 sec, so .
The fastest 10% are to be given advanced training. What task times qualify individuals for such training?
This is the value of X when Z has a pvalue of 0.90.
Z has a pvalue of 0.90 when it is between 1.28 and 1.29. So we want to find X when .
So
A task time of 177.125s qualify individuals for such training.