Heights of women follow a normal distribution with mean =63.6inches and standard

Question

Heights of women follow a normal distribution with mean =63.6inches and standard deviation of =2.5 inches. Please use this information to answer the next 3 questions.

1) Use the 68-95-99.7 Rule to estimate the percentage of women that are between 61.1 inches and 66.1 inches tall. (Please give your answer as a percentage, but don't include the percent sign.)

Suppose random samples of 10 women are chosen and their mean height calculated. Please calculate the mean and standard deviation of the distribution of all such sample means. Input your answers in the next two questions.

1) what is the mean?

2) what is the median?

Explanation / Answer

a)

mean=63.6 inches

standard deviation(sd)=2.5 inches.

so the interval is =mean +- sd=63.6+-2.5

so the interval is = 61.1 to 66.1 inches

we want  to estimate the percentage of women that are between 61.1 inches and 66.1 inches tall which is exactly equal to the calculated interval.

So by the 68-95-99.7 Rule,  percentage of women that are between 61.1 inches and 66.1 inches tall is 68.

b)

Sample mean=(63.4+62.5+64+62+60+62.5+66+65.4+62.3+66.1)/10

Mean=Median =63.42

Standard deviation =sqrt(1/10((63.4-63.42)^2+(62.5-63.42)^2+(64-63.42)^2+(62-63.42)^2+(60-63.42)^2+(62.5-63.42)^2+(66-63.42)^2+(65.4-63.42)^2+(62.3-63.42)^2+(66.1-63.42)^2))

Standard deviation =1.96

No Sample height (inches) 1 63.4 2 62.5 3 64 4 62 5 60 6 62.5 7 66 8 65.4 9 62.3 10 66.1

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