Biostats SDS 328M Homework 3

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Biostats SDS 328M Homework 3 1. The wingspans of adult seaside sparrows (Ammodramus maritimus) follow a normal distribution with a mean of 6.5 inches and a standard deviation of 0.3 inches. a. Sketch the distribution of seaside sparrow wingspans. Be sure to include labels and an accurate scale. (2pt) b. Between which two wingspan measurements are the middle two quartiles of the distribution? (3pt) Here, the wingspans of adult seaside sparrows , 𝑿 ~ 𝑵𝒐𝒓𝒎𝒂𝒍 ( 𝝁 = 𝟔 . 𝟓 , 𝝈 = 𝟎 . 𝟑 ) . Let Q 1 is the first quartile of the distribution of wingspans of adult seaside sparrows .  P ( X ≤ Q 1 ) = 0. 25  P [( X – μ) /  ≤ ( Q 1 – μ) /  ] = 0. 25  P [ Z ≤ ( Q 1 – 6. 5 ) / 0.3 ] = 0.25  (1) From normal areas table, P [ Z ≤ – 0. 67 ] = 0.25  (2) Comparing (1) and (2)  [ ( Q 1 – 25 ) / 4 ] = – 0. 67  Q 1 = 6.5 5 – 0. 67 ( 0.3 ) = 6.299
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