Question 1195496
for a single sample, your z-score is equal to (565.7 - 502) / 111 = .5738738739, rounded to 10 decimal places.
the probability she will get a z-score less than that is equal to .7169734661.
the probability she will not get a z-score less than that is equal to 1 minus .7169734661 = .2830265339.
that's the probability she will get a z-score greater than or equal to that.
all numbers are rounded to the number of decimal places that can be displayed from the calculator used.
round to 4 decimal places to get .2830.


for a single sample, you use the standard deviation.
for the mean of a sample of size greater than 1, you use the standard error.
if the sample size is 19, then the standard error is equal to the standard deviation divided by the square root of the sample size = 111 / sqrt(19) = 25.46514646.
the z-score is equal to (565.7 - 502) / 25.46514646 = 2.501458223.
the probability she will get a z-score less than that is equal to .9938158335.
the probability that she will not get a z-score less than that is equal to 1 - .9938158335 = .006184665.
that's the probability she will get a z-score greater than or equal to that.
round to 4 decimal places to get .0062.


a probability of .0062 is a very small probability.
that means that it is highly unlikely that a sample of 19 women will have a mean score of 565.7 or greater by chance alone.
that means that, if the mean of the sample of 19 women was 565.7, then something else might be influencing that other than chance.
a likely culprit would be that the preparation course did have an effect on their scores.


i used the ti-84 plus calculator to get these results.
you can get comparable results using the calculator at <a href = "https://www.calculator.net/z-score-calculator.html" target = "_blank">https://www.calculator.net/z-score-calculator.html</a>


results from using this calculator are:


<img src = "http://theo.x10hosting.com/2022/071501.jpg" >


<img src = "http://theo.x10hosting.com/2022/071502.jpg" >


let me know if you have any questions.
theo