Answer :
Final answer:
The probability of the high temperature being between 36 degrees Fahrenheit and 46 degrees Fahrenheit in January is approximately 0.6006 or 60.06%.
Explanation:
The student is asking for the probability that the high temperature on a given day in January will fall between 36 degrees Fahrenheit and 46 degrees Fahrenheit, given that the high temperatures are Normally distributed with a mean of 38 degrees Fahrenheit and a standard deviation of 5 degrees Fahrenheit.
To calculate this probability, we need to find the z-scores corresponding to the temperatures 36°F and 46°F and then use a standard Normal distribution table or calculator to find the probability between these z-scores.
The z-score for 36°F is (36 - 38) / 5 = -0.4.
The z-score for 46°F is (46 - 38) / 5 = 1.6.
Looking up these z-scores in a standard Normal distribution table or using a calculator, we can find the probability that the temperature is between these two z-scores.
Assuming the standard Normal distribution values, the probability for z = -0.4 is approximately 0.3446, and for z = 1.6 is approximately 0.9452.
Therefore, the probability of the temperature being between 36°F and 46°F is 0.9452 - 0.3446 = 0.6006.
