Quant Question Explanation please question, standard, average, between, correct

TheMBAGlover

Guy's, I am having trouble understanding the answer for this question, could someone please shed some light on this. Thanks.

The average amount of snow that falls during January in Frostbite Falls is normally distributed with a mean of 35 inches and a standard deviation of 5 inches. The probability that the snowfall amount in January of next year will be between 40 inches and 26.75 inches is closest to:

A) 79%.

B) 87%.

C) 68%.


Your answer: C was incorrect. The correct answer was A) 79%.


To calculate this answer, we will use the properties of the standard normal distribution. First, we will calculate the Z-value for the upper and lower points and then we will determine the approximate probability covering that range. Note: This question is an example of why it is important to memorize the general properties of the normal distribution.

Z = (observation – population mean) / standard deviation

Z26.75 = (26.75 – 35) / 5 = -1.65. (1.65 standard deviations to the left of the mean)
Z40 = (40 – 35) / 5 = 1.0 (1 standard deviation to the right of the mean)
Using the general approximations of the normal distribution:

68% of the observations fall within

Maddin

Draw a normal distribution with 35 being the centre. Question is asking for the probability that the rainfall is between 26.75 and 40. Add these 2 values on the distribution.

Now, convert these 2 values to Z and find the area under the curve between them.

scr879

look at the Z value for for 1, its .8413,
84.13% probability that the snowfall amount in January next year will fall below 40 inches

find the z value for -1.65 which is .0495, meaning 4.95% chance snow will be below 26.75 inches next year.

So to find whats going down in between take the .8413-.0495=.79