Question

Need a Hand with this practice problem!

A game is played with a spinner on a circle, like the minute hand on a clock. The circle is marked evenly from 0 to 100, so, for example, the 3:00 position corresponds to 25, the 6:00 position to 50 and so on. The player spins the spinner, and the resulting number is the number of seconds he or she is given to solve a word puzzle.

If 100 players are randomly selected, what is the approximate probability that the average time these players will get to solve the puzzle is between 44 and 56 seconds?

Answer 1

as time is distriuted between 0 to 100 seconds uniformrly therefore paramter a=0 and b=100

mean time for a person =(a+b)/2=50

and std deviation=(b-a)/sqrt(12)=28.8675

therefore for 100 players ; expected mean time =50

and std error of mean =std deviation/sqrt(n)=28.8675/sqrt(100)=2.887

from normal approximation: approximate probability that the average time these players will get to solve the puzzle is between 44 and 56 seconds =P(44<Xbar<56)

=P((44-50)/2.887<Z<(56-50)/2.887)=P(-2.08<Z<2.08)=0.9812-0.0188 =0.9624