jaxheisjax532
20.07.2020 •
Mathematics
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.2 inches, and standard deviation of 3.3 inches.
A) What is the probability that a randomly chosen child has a height of less than 63.75 inches? Answer= (Round your answer to 3 decimal places.)
B) What is the probability that a randomly chosen child has a height of more than 60 inches? Answer= (Round your answer to 3 decimal places.)
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Ответ:
A) 0.989
B) 0.875
Step-by-step explanation:
Let the X denote height measurements of ten year old children.
Thus, X follows the Normal distribution with mean = 56.2 inches and standard deviation = 3.3 inches.
A) we have to find the probability that a randomly chosen child has a height of less than 63.75 inches.
That is;
P(X < 63.75)
using z score formula, we have;
Z = (X - μ)/σ
Where, μ is mean and σ is standard deviation.
Thus;
Z = (63.75 - 56.2)/3.3
Z = 2.288
From z distribution table, we have the value as approximately 0.989
B) Similarly, using z score formula, we have;
Z = (X - μ)/σ
Where, μ is mean and σ is standard deviation.
Thus;
we have to find the probability that a randomly chosen child has a height of more than 60 inches.
Z = (60 - 56.2)/3.3
Z = 1.1515
From z-tables, the value is approximately 0.875
Ответ: