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

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 54.6 inches, and standard deviation of 1.4 inches.

What is the probability that the height of a randomly chosen child is between 52.9 and 55 inches? Do not round until you get your your final answer, and then round to 3 decimal places.

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Answer #1

Let the variable X denotes height measurements of ten year old children.

X follows Normal distribution with mean = 54.6 inches and standard deviation = 1.4 inches.

We have to find probability that height of randomly chosen child is between 52.9 and 55 inches.

That is P(52.9 < X < 55).

By using z score formula, Z = rac{X - mu }{sigma }

Where, mu is mean and sigma is standard deviation.

P(52.9 < X < 55) = 52.9-54.6 , X-μ , 55-54.6 P( 1.4 1.4

= P(-1.2143 < Z < 0.2857)

= P( Z < 0.2857) - P(Z < -1.2143)

= 0.612445 - 0.112316 .................... (Using Excel)

= 0.500129

~ 0.500

Hence, P(52.9 < X < 55) = 0.500

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