Water permeability of concrete can be measured by letting water flow across the surface and determining the amount lost (in inches per hour). suppose that the permeability index x for a randomly selected concrete specimen of a particular type is normally distributed with mean value 1000 and standard deviation 150. how likely is it that a single randomly selected specimen will have a permeability index between 550 and 1300?

97.59% probability that a single randomly selected specimen will have a permeability index between 550 and 1300.

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:

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:

.

How likely is it that a single randomly selected specimen will have a permeability index between 550 and 1300?

This is the pvalue of Z when X = 1300 subtracted by the pvalue of Z when X = 550.

Z = 1300

has a pvalue of 0.9772

Z = 550

has a pvalue of 0.0013

So there is a 0.9772 - 0.0013 = 0.9759 = 97.59% probability that a single randomly selected specimen will have a permeability index between 550 and 1300.

-2/