The z-statistic for an individual woman's height x = (x - population mean)/ population std dev
The z-statistic for the mean (Xbar) of a sample of size 22 = (Xbar - population mean)/(std dev/sqrt(n))
Since x = Xbar, the only difference between the two z statistics is the denominator.
Since Std dev is greater than std dev/sqrt(n), the denominator in the z-statistic for the mean (Xbar) will be smaller than the denominator in the z-statistic for the individual woman's height.
Consequently, the z-statistic for mean will be larger than the z-statistic for the individual woman.
To determine which event is more likely (single woman height < population mean or sample mean height < population mean), we check the probability of each z-statistic being less than the computed value.
Since there is a greater probability the z-statistic will be less than a larger value, you are more likely to select a sample of 22 women with the indicated mean.
