Answer:
1.) 92.61%
2.) 97.58%
3.) 65.06%
Step-by-step explanation:
Mean populational weight (X) = 175 pounds
Standard deviation (σ) = 7.6 pounds
The z-score for any given student weight, X, is defined by:

The z-score can be converted to a percentile of the normal distribution through a z-score table.
1.
The z-score for X=186 pounds is:

A z-score of 1.447 corresponds to the 92.61-th percentile.
Therefore, the probability that a male student weighs at most 186 pounds is:

2.
The z-score for X=160 pounds is:

A z-score of 1.447 corresponds to the 2.42-th percentile.
Therefore, the probability that a male student weighs at least 160 pounds is:

3.
The z-score for X=165 pounds is:

A z-score of -1.316 corresponds to the 9.41-th percentile.
The z-score for X=180 pounds is:

A z-score of 0.658 corresponds to the 74.47-th percentile.
Therefore, the probability that a male student weighs between 165 and 180 pounds is:
