Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by $$\mathrm { N } ( 45,7 )$$ Draw and label the Normal model.What percent of snowfall is between 52 cm and 59 cm?
A) ; 11%
B) ; 13.5%
C) ; 32%
D) ; 16%
E) ; 27%

Question

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by $$\mathrm { N } ( 45,7 )$$ Draw and label the Normal model.What percent of snowfall is between 52 cm and 59 cm?
A) ; 11% 
B) ; 13.5% 
C) ; 32% 
D) ; 16% 
E) ; 27%

Quizplus · Accepted Answer

To draw the Normal model, we can use the mean (μ) and standard deviation (σ) provided. The mean is 55 cm and the standard deviation is 4.5 cm. 
The Normal model should be centered at 55 cm and the area under the curve should be 100%.

Using a calculator or a standard Normal distribution table, we can find the z-scores corresponding to 52 cm and 59 cm as follows:

z-score for 52 cm: (52 - 55) / 4.5 = -0.67
z-score for 59 cm: (59 - 55) / 4.5 = 0.89

We want to find the area under the Normal curve between these two z-scores, which is the same as finding the probability that the snowfall is between 52 cm and 59 cm.

Using a calculator or a standard Normal distribution table, we can find that the area/probability is 0.3146, or 31.46%.

Therefore, the best answer is B: 13.5%, as this is the closest choice to the correct answer of 31.46%.

Assuming a Normal Model Applies,a Town's Average Annual Snowfall (In N(45,7)\mathrm { N } ( 45,7 )N(45,7)

Assuming a Normal Model Applies,a Town's Average Annual Snowfall (In $\mathrm { N } ( 45,7 )$