SOLUTION: The average daily maximum temperatures in March are 3�C in Montreal with a standard deviation of 3�C, and an average of2�C in Calgary with a standard deviation of 8�e. 1.During

Question 246742: The average daily maximum temperatures in March are 3�C in Montreal with a standard deviation of 3�C, and an average of2�C in Calgary with a standard deviation of 8�e.
1.During a cold snap Montreal has a high of -4�C and Calgary a high of-lO�e. Assuming the daily maximum temperatures are normally distributed, which city has the 'colder snap'? Explain with words and calculations.
2.What is the probability that Montreal would have a maxi~umtemperature between -2�C and 7�C in March?
3. The maximum temperature in Calgary such that only 5% ofdays have a maximum temperature higher than this is:
4. The two maximum temperatures in March for Montreal that represent the middle 80% oftemperatures are:
a) (0.48, 5.52) b) (1.935, 7.935) c) (-8.256, 12.256) d) (-0.846,6.846)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The average daily maximum temperatures in March are 3�C in Montreal with a standard deviation of 3�C, and an average of 2�C in Calgary with a standard deviation of 8�e.
1.During a cold snap Montreal has a high of -4�C and Calgary a high of-lO�C. Assuming the daily maximum temperatures are normally distributed, which city has the 'colder snap'? Explain with words and calculations.
---
Montreal: z(-4) = (-4-3)/3 = -7/3 = -2 1/3
Calgary: z(-10) = (-10-2)/8 = -12/8 = -3/2 = -1.5
The Montreal high was further below the average so Montreal had the
colder snap.
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2.What is the probability that Montreal would have a maximum temperature between -2�C and 7�C in March?
"average daily maximum temperatures in March are 3�C in Montreal with a standard deviation of 3�C"
z(-2) = (-2-3)/3 = -5/3 = -1 2/3
z(7) = (7-3)/3 = 4/3 = 1 1/3
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P(-2 < x < 7) = P(-5/3 < z < 4/3) = 0.8610
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3. The maximum temperature in Calgary such that only 5% of days have a maximum temperature higher than this is:
"average daily maximum temperatures in March are 3�C in Montreal with a standard deviation of 3�C
The z-value that has 5% above it is 1.645
x = 1.645*3 + 3 = 7.935
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4. The two maximum temperatures in March for Montreal that represent the middle 80% oftemperatures are:
Find the z-value that has two tails of 10% each.
z = 1.2816
x = 1.2816*3+3 = 6.846
x = -1.2816*3+3 = -0.846

a) (0.48, 5.52) b) (1.935, 7.935) c) (-8.256, 12.256) d) (-0.846,6.846)
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Cheers,
Stan H.

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