Answer:
0.9544
Step-by-step explanation:
Mean = μ=57
Standard deviation σ=2
Formula : [tex]z=\frac{x-\mu}{\sigma}[/tex]
At x = 53
[tex]z=\frac{53-57}{2}[/tex]
[tex]z=-2[/tex]
Refer the z table
P(z<-2)=0.0228
At x = 61
[tex]z=\frac{61-57}{2}[/tex]
[tex]z=2[/tex]
Refer the z table
P(z<2)=0.9772
We are suppose to find the probability that the height of a randomly selected 5th grade boy will be between 53 inches and 61 inches.
P(53<x<61)=P(-2<z<2)=P(z<2)-P(z<-2) = 0.9772 - 0.0228=0.9544
Hence the probability that the height of a randomly selected 5th grade boy will be between 53 inches and 61 inches is 0.9544