A box of tickets averages out to 75 and the SD is 10. One hundred draws are made at random with replacement from this box.

Question

a)Find the chance that the average of the draws will be in the range 65 to 85.
b)repeat for the range 74 to 76.

Answer 1

Use z-scores and a z-table for this problem. Because you are given a sample size, you will need to include the sample size in the calculation:

z = (x - mean)/(sd/√n)

For a):
This will be very close to 100% chance that the average of the draws will be in the range listed (z-scores will be very large).

For b):
z = (74 - 75)/(10/√100)
z = (76 - 75)/(10/√100)

Finish the calculation for both z-scores. Use the z-table to find the probability between the two scores.

I hope this will help get you started.