The weights of a large number of miniature poodles are approximately normally distributed with a mean of 8 kilograms and a standard deviation of 0.9 kilogram. if measurements are recorded to the nearest tenth of a kilogram, find the fraction of these poodles with weights

Using the normal distribution, it is found that:

The z-score is:

The probability of finding a value less than X is the p-value of Z.The probability of finding a value more than X is the p-value of Z.The probability of finding a value between a and b is the p-value of Z when X = b subtracted by the p-value of Z when X = a.

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

It 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, which is the percentile of X.

In this problem:

Mean of 8, thus Standard deviation of 0.9, thus .

The z-score will be given by:

Applying the percentile concept:

The probability of finding a value less than X is the p-value of Z.The probability of finding a value more than X is the p-value of Z.The probability of finding a value between a and b is the p-value of Z when X = b subtracted by the p-value of Z when X = a.

A similar problem is given at link