Heights of 10 year-olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. Which of the following is true? Roughly 95% of 10 year-olds are between 37 and 73 inches tall. A 10 year-old who is 65 inches tall would be considered more unusual than a 10 year-old who is 45 inches tall. A normal probability plot of heights of a random sample of 500 10 year - olds people should show a fairly straight line. We would expect more 10 year-olds to be shorter than 55 inches than taller

Question

Mathematics

Cade Barnes

6 December, 15:15

Heights of 10 year-olds, regardless of gender, closely follow a normal distribution with mean 55 inches and standard deviation 6 inches. Which of the following is true? Roughly 95% of 10 year-olds are between 37 and 73 inches tall. A 10 year-old who is 65 inches tall would be considered more unusual than a 10 year-old who is 45 inches tall. A normal probability plot of heights of a random sample of 500 10 year - olds people should show a fairly straight line. We would expect more 10 year-olds to be shorter than 55 inches than taller

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Reece Shepard · Answer 1

A normal probability plot of heights of a random sample of 500 10 year - old people should show a fairly straight line

Step-by-step explanation:

We are given that heights are normally distributed with mean=55 and standard deviation=6.

Now explaining all the given statements.

Roughly 95% of 10 year-old are between 37 and 73 inches tall.

This statement is not true. We know that approximately 95% of data lies within interval mean±2*standard deviation (empirical rule).

mean±2*standard deviation=55±2*6=55±12 = (43,67)

So, 95% of 10 year-old are between 47 and 67 inches tall. Thus, the above statement is wrong.

A 10 year-old who is 65 inches tall would be considered more unusual than a 10 year-old who is 45 inches tall.

If the heights of 10 years old lie more than 2 standard deviation away then it will considered as unusual and If the heights of 10 years old lie more than 3 standard deviation away then it will considered as more unusual.

As 65 and 475 lies within two standard deviation from mean, so these are not unusual data values. So, the above statement is not true.

A normal probability plot of heights of a random sample of 500 10 year - old people should show a fairly straight line.

A normal probability plot shows straight line when the data is normally distributed and we know that if the population is normally distributed then then sample selected from this population is also normally distributed with mean μxbar and standard deviation σxbar. So, this statement is true.

We would expect more 10 year-old to be shorter than 55 inches than taller than 55 inches

Last few words were missing from the statement and i gathered them through web search.

The probability of 10 years old shorter than 55 is 50% and probability of 10 years old taller than 55 as area under the normal curve is 1 and given mean is 55. The area above mean and below mean in the normal curve is 0.5. So, we can't say that We would expect more 10 year-old to be shorter than 55 inches than taller than 55 as they have equal probabilities. Thus, the above statement is not true.