Answer:
P = 0.9544
Step-by-step explanation:
Firs,t we need to standardize 46 and 54 using the following equation:
![z=\frac{x-m}{s}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-m%7D%7Bs%7D)
Where m is the mean and s is the standard deviation for the random variable.
Replacing m by 50 and s by 2, we find that 46 and 54 are equivalent to:
![z=\frac{46-50}{2}=-2\\z=\frac{54-50}{2}=2](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B46-50%7D%7B2%7D%3D-2%5C%5Cz%3D%5Cfrac%7B54-50%7D%7B2%7D%3D2)
Then, the probability that x is between 46 and 54 is equal to:
P(46<x<54) = P(-2<z<2)
So, using the normal table, we can find the probability as:
P(-2<z<2) = P(z<2) - P(z<-2)
P(-2<z<2) = 0.9772 - 0.0228
P(-2<z<2) = 0.9544