Question

The average low temperature in December in City A is 45 degrees, with a standard deviation of 10 degrees. The average low temperature in December in City B is 46 degrees, with a standard deviation 4 degrees.  Please answer 2 questions from the options below. Please vary the questions you answer so not everyone answers the same ones. Then read and comment on a student by either agreeing or disagreeing with something they answered, politely ofcourse:

2. What percentage of days in December in City B will have low temperatures above 50 degrees? How did you determine this? (Please refer to the Empirical Rule chart in your notes)

3. What low temperature in City A would correspond to a z score of -2? What does this mean?

Answer 1

(2)

City B;

= 46

= 4

To find P(X>50):

Z = (50 - 46)/4 = 1

From Empirical Rule Chart:

Approximately 68% of data lies within 1 standard deviation from mean.

So,

1 - 0.68 = 0.32 of the data lie outside 1 .standard deviation from mean.

So,

0.32/2 = 0.16 of data lie above + 1 standard deviation from mean.

So,

P(X>50) = 0.16

So,

Answer is:

0.16

(3)

City A:

= 45

= 10

Z = - 2 = (X - 45)/10

So,

X = 45 - (2 X 10) = 25

So,

Answer is:

25

This means that there is 95% chance that the low temperature in City A is 25 degrees,