Statistics math question

Question

a physics class of 50 students measured thier heights. thier average height was 71 inches with a standard deviation of 5. suppose a 51st student enters the room. find the height in inches of the 51st students that the average height is 70.5

Answer 1

Since the average height is the total height divided by the total number of students, we can write this equation:

(71)(50) + x = 70.5

51

Where x = the height of the 51st student and (71)(50) is the total height of the first 50. If we solve the equation for x, we have

x = (70.5) (51) - (71) (50)

x = 45.5 inches