Answer:
A) 0.46452
B) 0.82064
Explanation:
We solve for question A and B using z score formula
z = (x - μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
A) What is the probability that a randomly chosen child has a height of less than 52.85 inches?
x = 52.85 inches, μ = 53.5 inches, σ = 7.3 inches
z = (x - μ)/σ
= 52.85 - 53.5 / 7.3
= -0.08904
Using the z table to find the probability of the z score above.
P(x<52.85) = 0.46452
Therefore, the probability that a randomly chosen child has a height of less than 52.85 inches is 0.46452
B) What is the probability that a randomly chosen child has a height of more than 46.8 inches?
x = 46.8 inches, μ = 53.5 inches, σ = 7.3 inches
z = (x - μ)/σ
= 46.8 - 53.5 / 7.3
= -0.91781
Using the z table to find the probability of the z score above.
P(x<46.8) = 0.17936
P(x>46.8) = 1 - P(x<46.8)
= 1 - 0.17936
= 0.82064
Therefore, the probability that a randomly chosen child has a height of more than 46.8 inches is 0.82064