Question

17)Here is the set of data from the previous page:10,11,12,13,15,17,17,18,20,20. The first, second, and third quartiles for this data set are 12, 16, and 18 respectively. Identify the 5-number summary for this data set, and create a box plot(box-and-whisker plot) representing it.

18)a) What 3 numbers are cited in the Empirical Rule for normal distributions?(b) Suppose that height for a species of tree is normally distributed with a mean of 30 feet and a standarddeviation of 3 feet. Approximately what percentage of trees of that species are between 27 and 36 feet tall?

19)Suppose that you have 5 bags of rocks. The first four contain 13, 14, 15, and 16 rocks respectively.Will thestandard deviationof the contents of the 5 bags belargerif the 5th bag contains 1 rock, or if it contains16 rocks? Explain why.

20)(a) What is the formula for the angle that determines a slice of a pie chart?(b) In an experiment, what is the group thatdoesn’treceive a treatment called?(c) Suppose a sample has a variance of 81. What is its standard deviation?

21)(a) What is the formula for the angle that determines a slice of a pie chart?(b) In an experiment, what is the group thatdoesn’treceive a treatment called?(c) Suppose a sample has a variance of 81. What is its standard deviation?

Answer 1

Q17:

5 point summary:

Minimum = 10

First quartile, Q1 = 12

Median =16

Third quartile, Q3 =18

Maximum = 20

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18 a)

The empirical rule states that for a normal distribution:

68% of the data will fall within one standard deviation of the mean.

95% of the data will fall within two standard deviations of the mean.

Almost all (99.7%) of the data will fall within three standard deviations of the mean.

b)

µ = 30, σ = 3

z = (X-µ)/σ = (27-30)/3 = -1

z = (X-µ)/σ = (36-30)/3 = 2

percentage of trees of that species are between 27 and 36 feet tall = (68)/2 + (95)/2 = 81.5%

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19.

The standard deviation will be larger if the 5th bag contains 1 rock. As then the range of rock in the bags will be larger and the range increase the standard deviation increases

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20. a) formula for the angle that determines a slice of a pie chart = proportion of that slice *360 degree

b) Placebo

c) Standard deviation= sqrt(81) = 9