Question

Shown on the pages below are the normal quantile plots and histograms of three fast food restaurants that represent service times during dinner hours. The green vertical line in each histogram represents the mean, the red represents the median. Summary statistics for the three restaurants are also given. Compare and contrast the three restaurants service times as compared to a normal distribution. Write your answers in complete sentences. Write your answers on this page, below the summary statistics. Use additional pages if needed.

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Dunkin Donuts Dinner Normal: Mean 128.28, SD 62.948 Frequency 10 300 DUNKIN DONUTS DINNER Normal Quantile DUNKIN DONUTS DINNER Wendy's Dinner arに Frequency 50 100 200 WENDYS DINNER Normal Quantile 150 WENDYS DINNER 250 Burger King Dinner ormal: Mean1 Frequency 15 10 100 BURGER KING DINNER Normal Quantile 100 150 BURGER KING DINNER 250 19- 20 (20 points) Shown on the pages below are the normal quantile plots and histograms for three fast food restaurants that represent service times during dinner hours. The green vertical line in each histogram represents the mean, the red represents the median. Summary statistics for the three restaurants are also given. Compare and contrast the three restaurants service times as compared to a normal distribution. Write your answers in complete sentences. Write your answers on this page, below the summary statistics. Use additional pages if needed Summary statistics: n Mean Std. dev. Median Range Min Max Q1 Q3 IQR BURGER KING DINNER 50 153.3 49.789865 143 239 54 293 127172 45 50 142.58 55.925274 132 211 56 267 101 165 64 DUNKIN DONUTS DINNER 50 128.28 62.948323 113.5 289 44 333 85160 75 Column WENDYS DINNER Class width on all histograms is 20.

Answer 1

Let us first discuss few properties of the normal distribution:

1) The mean, median and mode are at the same point in a normal distribution curve.

2) Probability at the mean point is 0.5 i.e. it is symmetric about mean and divides the curve into two halves.

3) A normal distribution curve has Kurtosis equal to 3 which defines the shape and peak of the curve. the tails show the extreme values that have a very low probability of occuring.

Now, in relation to the question, clearly for none of the restaurants the mean median and mode are equal.

For Dunkin Donuts we can roughly say that the mean is at the position of the normal mean but median is slightly less than that is required for it to be normally distributed.

For Wendy's dinner, the curve looks very peaked, thus the kurtosis is greater than 3 in contrast to the normal curve which is equal to 3. This shows accumulation of alot of values in the center and a lighter tail, more like student's T-distribution.

For Burger King Dinner too the median and mean differ and the data seems to be positively skewed, which contrasts with normal distribution.