Answer:
[tex]X =4.94\ in[/tex]
Step-by-step explanation:
For a standard normal distribution of mean [tex]\mu_z = 0[/tex] and [tex]\sigma_z = 1[/tex]
the statistic [tex]Z = \frac{X - \mu}{\sigma}[/tex]
In this problem we look for the value of X that is 2 standard deviations above the mean.
If there are two standard deviations above the mean, then, in the standard normal distribution, the statistic [tex]Z = 2[/tex].
Then, we clear X.
[tex]2 = \frac{X -\mu}{\sigma}\\\\2\sigma = X - \mu\\\\\2\sigma + \mu = X\\\\[/tex]
Where:
[tex]\sigma=0.52\\\\\mu=3.9\\\\X = 2(0.52) + 3.9\\\\X =4.94[/tex]
