SOLUTION: The average summer temperature in Anchorage is 69°F. If the daily temperature is normally distributed with a standard deviation of 7°F, what percentage of the time would the temp

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Question 1180209: The average summer temperature in Anchorage is 69°F. If the daily temperature is normally distributed with a standard deviation of 7°F, what percentage of the time would the temperature be between 55°F and 76°F?
a. 34.0%
b. 47.5%
c. 68.0%
d. 81.5%
e. 99.7%
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


Use your 68-95-99.7 rule to get the answer.

69-55=14=2(7); 55 degrees is 2 standard deviations below the mean.

76-69=7; 76 degrees is 1 standard deviation above the mean.

68% of readings are within 1 standard deviation of the mean, so 34% of readings are between the mean and a reading 1 standard deviation above the mean. So in this problem 34% of the readings are between 69 and 76 degrees.

95% of readings are within 2 standard deviations of the mean, so 47.5% of readings are between the mean and a reading 1 standard deviations below the mean. So in this problem 47.5% of the readings are between 55 and 69 degrees.

So the percentage of readings between 55 and 76 degrees is 34+47.5=81.5%.

ANSWER d.