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Leya [2.2K]
3 years ago
6

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally dis

tributed with a mean of 55.4 inches, and standard deviation of 4.1 inches.
A) What is the probability that a randomly chosen child has a height of less than 61.25 inches?

Answer= (Round your answer to 4 decimal places.)

B) What is the probability that a randomly chosen child has a height of more than 46.5 inches?

Answer= (Round your answer to 4 decimal places.)
Mathematics
1 answer:
aliya0001 [1]3 years ago
5 0

(A)

P(<em>X</em> < 61.25) = P((<em>X</em> - 55.4)/4.1 < (61.25 - 55.4)/4.1)

… ≈ P(<em>Z</em> ≤ 0.1427)

… ≈ 0.5567

(B)

P(<em>X</em> > 46.5) = P((<em>X</em> - 55.4)/4.1 > (46.5 - 55.4)/4.1)

… ≈ P(<em>Z</em> > -2.1707)

… ≈ 1 - P(<em>Z</em> ≤ -2.1707)

… ≈ 0.9850

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