I'm supposed to find the first and third quartiles of a Normal distribution with the mean 0.785 millimeters (mm) and standard deviation 0.071 mm.

answered 5 days ago by Level 10 User (53,200 points)

When you look in the body of a normal distribution table you can find the Z scores corresponding to 0.25 and 0.75. The Z score tells you how many standard deviations from the mean correspond to the Z scores. From this you can work out Q1 and Q3.

For Q1 Z=-0.675 and for Q3 Z=0.675. Z is calculated from the mean and standard deviation: Z=(X-m)/SD=(X-0.785)/0.071=0.675. |X-0.785|=0.675*0.071=0.048mm, making X=0.833mm for Q3 and 0.785-0.048=0.737mm for Q1.

Q1=0.737mm and Q3=0.833mm.

In a normal distribution half the data are below the mean and median (Q2) and half are above. The values we calculated for Q1 and Q3 divide the range into quartiles. A quarter of the data are below Q1 and above Q3. The interquartile range Q1 to Q3 contains half the data.

answered 4 days ago by Top Rated User (415,140 points)