Question

The heights of boys in a grade 10 class are normally distributed with a mean of 168 cm and a standard deviation of 2.5 cm. In which range do 95% of the heights approximately fall? A. 163 - 173 cm B. 160.5 - 168 cm C, 160.5- 175.5 cm D, 163 - 175.5 cm

Answer 1

To determine the range in which 95% of the heights fall, we can use the empirical rule for a normal distribution. The range is approximately from 163 cm to 173 cm.

Step-by-step explanation:

To determine the range in which 95% of the heights fall, we can use the empirical rule for a normal distribution. According to the empirical rule, approximately 95% of the data falls within 2 standard deviations of the mean. In this case, the mean height is 168 cm and the standard deviation is 2.5 cm. Therefore, 2 standard deviations above and below the mean would be 2 x 2.5 = 5 cm.

So, the range in which 95% of the heights approximately fall is from 163 cm (168 cm - 5 cm) to 173 cm (168 cm + 5 cm). Therefore, the correct answer is option A, 163 - 173 cm.

Answer 2

Using the empirical rule and the given mean and standard deviation, approximately 95% of the boys' heights in the class fall between 163 cm and 173 cm, which corresponds to option A.

Step-by-step explanation:

The range of heights where approximately 95% of the boys fall in a normally distributed set with a mean of 168 cm and a standard deviation of 2.5 cm can be found using the empirical rule. This rule states that about 95% of the data falls within two standard deviations from the mean. To calculate this range, we add and subtract two standard deviations from the mean.

Calculations:
Mean (M) = 168 cm
Standard Deviation (SD) = 2.5 cm
Range for 95%: M ± 2*SD
Lower bound = M - 2*SD = 168 - 2*2.5 = 168 - 5 = 163 cm
Upper bound = M + 2*SD = 168 + 2*2.5 = 168 + 5 = 173 cm

Therefore, about 95% of the heights will fall between 163 cm and 173 cm, which corresponds to option A.