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Answer :
Final answer:
The range covering the middle 95% of student weights is 109 to 181 pounds. Approximately 50% weigh less than 145 pounds (the median), and about 2.5% weigh more than 181 pounds. One-fourth of the students weigh less than 127 pounds.
Explanation:
The weights of students in a large statistics class follow a normal distribution with a mean of 145 pounds and a standard deviation of 18 pounds. To find the range that covers the middle 95% of the student weight, we use the empirical rule, which states that for a normal distribution about 95% of data falls within two standard deviations from the mean. Thus, the range is from 145 - 2(18) = 109 pounds to 145 + 2(18) = 181 pounds.
About 50% of the students weigh less than the mean of 145poundsn,becauses,e in a normal distribution, the mean is also the median, which divides the distribution into two equal halves.
To find the percentage of students who weigh more than 181 pounds, we use the empirical rule again and understand that approximately 2.5% of the students will fall above two standard deviations from the mean. Lastly, to find the weight that one-fourth of the students weigh less than we search for the first quartile, which for a normal distribution is approximately one standard deviation below the mean. Using this information, we calculate that one-fourth of the students weigh less than 145 - 18 = 127 pounds. The median weight for the students is 145 pounds.
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