Question 1198914
mean = 55
standard deviation = 8
want probability of scores between 47 and 71.


probability is .8166


use z-score if you don't have a calculator that does it directly.


z-score formula is z = (x - m) / s
x is the raw score
m is the mean
s is the standard deviation.


on the low side, formula becomes z = (47 - 55)/8 = -1
on the high side, formula becomes z = (71 - 55)/8 = 2


use a calculator or a z-score table to find the area to the left of those z-scores.


area to the left of z-score of -1 = .1586552
agea to the left of z-score of 2 = .9772499
area in between = larger area minus smaller area = .81859467
round to 4 decimal places to get .8186


the probability of getting a score between 47 and 71 is equal to .8186.
that's your answer.


a calculator i used to get the answer directly is found at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>


here are the results from using that calculator.


<img src = "http://theo.x10hosting.com/2022/120404.jpg">


calculator i used was the ti-84 plus.


you could also use the z-score table, but a calculator is much easier.