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The mean height of 500 students is 151 cm and the standard deviation is 15 cm. Assuming that the heights are normally distributed, find how many student’s height lie between 120 and 155 cms?
- a)291
- b)292
- c)294
- d)296
Correct answer is option 'B'. Can you explain this answer?
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To find how many students fall within a certain range of heights, we can use the concept of standard deviation.
First, we need to determine the number of standard deviations away from the mean the desired range is. Let's say we want to find the number of students within one standard deviation above and below the mean. Since the standard deviation is 15 cm, one standard deviation is also 15 cm.
To find the number of students within one standard deviation of the mean, we can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.
So, the number of students within one standard deviation of the mean is approximately 68% of 500 students:
0.68 * 500 = 340 students
Therefore, approximately 340 students fall within one standard deviation of the mean height.
First, we need to determine the number of standard deviations away from the mean the desired range is. Let's say we want to find the number of students within one standard deviation above and below the mean. Since the standard deviation is 15 cm, one standard deviation is also 15 cm.
To find the number of students within one standard deviation of the mean, we can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, approximately 68% of the data falls within one standard deviation of the mean in a normal distribution.
So, the number of students within one standard deviation of the mean is approximately 68% of 500 students:
0.68 * 500 = 340 students
Therefore, approximately 340 students fall within one standard deviation of the mean height.
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