Answer: Therefore, the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches is 0.884. Rounded to 3 decimal places, the answer is 0.884.
Step-by-step explanation:We can use the standard normal distribution to find the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches.
First, we need to standardize the values using the formula:
z = (x - mu) / sigma
where:
x = 52.2 and 60.6 (the values we want to find the probability between)
mu = 55.7 (the mean)
sigma = 2.6 (the standard deviation)
For x = 52.2:
z = (52.2 - 55.7) / 2.6 = -1.346
For x = 60.6:
z = (60.6 - 55.7) / 2.6 = 1.885
Next, we use a standard normal distribution table or calculator to find the area between these two z-scores:
P(-1.346 < z < 1.885) = 0.884
Therefore, the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches is 0.884. Rounded to 3 decimal places, the answer is 0.884.