Sprint LTE 7:14 PM mail-attachment.googleusercontent.com & Suppose the following

Question

Sprint LTE 7:14 PM mail-attachment.googleusercontent.com & Suppose the following histograms depict the distribution of daily temperatures in North Carolina and Massachusetts over 90 days of winter last year Summary Data Massachusetts 40 degrees degrees Sample Mean [ 55 degrees Sample Standard Deviation () 0 degrees a. In North Carolina, approximately what percentage of winter days had a daily b. In Massachusetts, approximately what percentage of winter days had a daly . What was the variance in the daily winter temperature in North Carolna? In temperature less than or equal to 50 degrees? temperature less than or equal to 50 degrees? Massachusetts? Which state had greater variability in daily winter temperature? For part (d), assume that the daily winter temperature in North Carolina and Massachunetts both follow an approximately normal (symmetric, mound-shaped) distribution. d. In January, you notice on the weather news that the temperature is going to be 30 degrees in either North Carolina or Massachusetts Is this temperature an outller with respect to North Carolina daily winter temperatures? With respect to Massachusetts daily winter temperature? Hint Base your answers on a z The percentage of NC winter days that had a daily temperature less than or equal to 50 degrees equals +32 22%. The percentage of MA winter days that had a daily temperature less than or equal to 50 degrees equals 1 -. 93.33%. The variance in the NC wnter temperatures was 00The variance in the MA winter temperatures was 49. The NC winter temperatures have greater variability

Explanation / Answer

Ans:

a)Assuming the approximate temperature distribution as Normal distribution:

z=(50-55)/10=-5/10=-0.5

z=-0.5

P(z<=-0.5)=0.3085

b)z=(50-40)/7=10/7=1.43

z=-1.43

P(z<=1.43)=0.9236

(answers are approximately same as calculated directly from histogram.)

c)variance for North carolina is 102=100

variance for Massachusetts is 72=49

North carolina temperature has greater variability.

d)

z score=-0.5 for North carlina

As,-3<z <3,so not outlier.

z score=1.43 for Massachusetts

As,-3<z <3,so not outlier.

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