The length of students' college careers at Anytown University is known to be Normally distributed, with a mean length of 5.5 years and a standard deviation of 1.75 years. What is the lower quartile for the length of students' careers at Anytown University? Use the fact that the middle 50% of the data falls within 0.67 standard deviations from the mean.

Question

Quizplus · Accepted Answer

The lower quartile represents the point below which 25% of the data falls. 
According to the given fact, the middle 50% of the data falls within 0.67 standard deviations from the mean. Therefore, the remaining 50% of the data will fall beyond this range. Half of this remaining data will fall below the mean, and half will fall above the mean. 
So, to find the lower quartile, we need to subtract half of the remaining 50% of the data from the mean. 
Half of 50% is 25%, which is the percentage below the lower quartile. 
Using a standard Normal distribution table, we can find that the Z-score corresponding to the lower quarter point is approximately -0.6745. 
Hence, the lower quartile can be calculated as: 
Lower quartile = Mean - (Z-score for lower quartile) × Standard deviation 
= 5.5 - (-0.6745) × 1.75 
= 5.5 + 1.1824 
= 6.6824 
Therefore, the lower quartile for the length of students' careers at Anytown University is approximately 4.3275 years (rounded to four decimal places).

The Length of Students' College Careers at Anytown University Is