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.)

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

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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answear:

a

step-by-step explanation: a