The average January temperature in Calgary varies from year to year. These avera

Question

The average January temperature in Calgary varies from year to year. These average January temperatures themselves have an average, over many past years of-8 2 degrees Celsius, with a standard deviation of 3.1 degrees Assume temperatures are normally distributed. (a) During what percentage of years does Calgary have a January average above 0 degrees? (b) In the 20% coldest Januaries, the average January temperature reaches no higher than how many degrees? (c) What is the probability that the average for the next five January temperatures will exceed -2 degrees? If this happens, would you consider this evidence of climatic warming (at least locally, in Calgary), or just normal variation? Explain your reasoning

Explanation / Answer

mean = -8.2 , s = 3.1

a)
P(X > 0)

z = ( x - mean) / s
= ( 0 - (-8.2)) / 3.1
= 2.645

we need to find P( z> 2.645)
P(X > 0 ) = P( z> 2.645) = 0.0041

b)

z value at 20% = 0.8416

x = mean + z * s
= -8.2 + 0.8416 * 3.1
= -5.5910

c)
P(X > -2)
z = ( x - mean) / s
= ( -2 - (-8.2)) / 3.1
= 2

we need to find P( z> 2)
P(X > -2) = P( z> 2) = 0.0228

P = 0.0228 = P^5
= ( 0.0228)^5 = 0.00000000616
If this happens its the indication of warming because probability calculated is very small almost equals to zero

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