Answer:
Probability that a randomly chosen 10-year-old is shorter than 48 inches 0.121 .
Step-by-step explanation:
We are given that heights of 10-year-old closely follow a normal distribution with mean 55 inches and standard deviation 6 inches i.e.;
Mean, [tex]\mu[/tex] = 55 inches    and   Standard deviation, [tex]\sigma[/tex] = 6 inches
Also, Â Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
Let X = a randomly chosen 10-year-old
Now, Probability(X < 48 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{48-55}{6}[/tex] ) = P(Z < -1.17)
                         = 1 - P(Z < 1.17) = 1 - 0.87900 = 0.121
The above probability is calculated using z table.
Therefore, the probability that a randomly chosen 10-year-old is shorter than 48 inches is 0.121 .
