A sample of stars from the constellation Orion which is usua

A sample of stars from the constellation Orion, which is usually visible in the night sky, is drawn. The following boxplot shows a summary of the stars\' magnitudes, which measures how bright or dim the star is. (Note that smaller magnitudes indicate a brighter star.)

(a) Use the box plot to give approximate values for the five-number summary.

(b) What does the box portion of the box plot suggest about possible skew?

no skew present
skewed to the right    
skewed to the left

(c) The mean star magnitude is 1.17 and the standard deviation is 0.56.

(i) Find the z-score associated with the maximum magnitude.
z =
(ii) What does this z-score indicate?

This z-score indicates that the maximum is 2.375 standard deviations below the mean.
This z-score indicates that the maximum is 2.375 standard deviations above the mean.    
This z-score indicates that the maximum is an outlier.

(NOTE: If you get part iii wrong below, a video will pop up that may help you answer the question. But remember that your values could be different from the values in the video due to randomization.)
(iii) What is the z-score for a value that is 1.197 standard deviations below the mean?
z-score =

(iv) What is the star magnitude associated with this z-score?
magnitude =

Solution

(a)

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(b)skewed to the left

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(c)(i) z =(X-mean)/s

= (X-1.17)/0.56

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(ii)This z-score indicates that the maximum is 2.375 standard deviations above the mean.

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(iii) z-score =1.197

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(iv.) z =(X-mean)/s

= (X-1.17)/0.56