the mean weigh of 500 male students at a certain college is 151 lb , and the standard deviation is 15 lb. assuming that the weights are normally distributed , how many students weigh more then 181 lb.
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To find out how many students weigh more than 181 lb, we need to calculate the z-score for this weight and then use the z-table (also known as the standard normal distribution table).
Here's how to calculate the z-score:
1. Subtract the mean weight from the specified weight: 181 - 151 = 30.
2. Divide the result by the standard deviation: 30 / 15 = 2.
The z-score for a weight of 181 lb is 2.
Now, we can look up the area under the normal distribution curve to the right of the z-score of 2 using the z-table.
The z-table provides the probability for values up to a specific z-score. To find the probability to the right of the z-score of 2, we need to subtract the table value from 1.
The closest z-score in the table is 2.0, which corresponds to an area of 0.9772. So, the probability to the left of the z-score of 2 is 0.9772.
To find the probability to the right of the z-score of 2, we subtract the table value from 1: 1 - 0.9772 = 0.0228.
Therefore, approximately 2.28% of the students weigh more than 181 lb.
To find the number of students who weigh more than 181 lb, we multiply the probability by the total number of students:
0.0228 * 500 ≈ 11.4
Since we cannot have a fraction of a student, we round up to the nearest whole number.
Therefore, around 12 students weigh more than 181 lb.