Answer: [tex]\mu=18[/tex] and [tex]\sigma= 1.5[/tex]
Step-by-step explanation:
Let [tex]\mu[/tex] = mean and [tex]\sigma[/tex] = standard deviation.
Given : If a set of data are normally distributed with at least 68% of scores falling between scores 16.5 and 19.5.
If these values mark the first standard deviation from the mean, then
[tex]\mu -\sigma=16.5----(1)\\\mu +\sigma=19.5-----(2)[/tex]
Adding (1) and (2) ,we get
[tex]2\mu=36\\\Rightarrow\ \mu=18[/tex]
Subtract (1) from (2) , we get
[tex]2\sigma= 3\\\Rightarrow\ \sigma= 1.5[/tex]
Hence, the values of the mean and standard deviation in this normal distribution are :
[tex]\mu=18[/tex] and [tex]\sigma= 1.5[/tex]
