Answer:
P = 0.9544
Step-by-step explanation:
Firs,t we need to standardize 46 and 54 using the following equation:
[tex]z=\frac{x-m}{s}[/tex]
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:
[tex]z=\frac{46-50}{2}=-2\\z=\frac{54-50}{2}=2[/tex]
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
