Answer :
Final answer:
The z-score for a temperature of 66 degrees is 1.6. The probability of the temperature being greater than 66 degrees is very small. The temperature that separates the bottom 10% is 52.6 degrees.
Explanation:
a. To find the z-score for a temperature of 66 degrees, you'd subtract the mean temperature of the lake from 66 and then divide by the standard deviation. So, Z = (66-58)/5 = 1.6.
b. When it comes to finding the probability of the temperature being greater than 66 degrees, it corresponds to finding the area under the curve of a normal distribution to the right of Z=1.6. This requires tables or statistical software to calculate accurately, but it will be quite small.
c. To find the temperature that separates the bottom 10% of the temperatures, we look for the Z score that corresponds to the 10th percentile. This is generally around -1.28 for a normal distribution. Thus, the temperature for the lower 10% of the distribution = mean + (Z*standard deviation) = 58 + (-1.28*5) = 52.6 degrees.
Learn more about Standard Distribution here:
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