SOLUTION: The diameter of a brand of​ Ping-Pong balls is approximately normally​ distributed, with a mean of 1.31 inches and a standard deviation of 0.04 inch. A random sample o

Algebra ->  Probability-and-statistics -> SOLUTION: The diameter of a brand of​ Ping-Pong balls is approximately normally​ distributed, with a mean of 1.31 inches and a standard deviation of 0.04 inch. A random sample o      Log On


   

Question 1112917: The diameter of a brand of​ Ping-Pong balls is approximately normally​ distributed, with a mean of 1.31 inches and a standard deviation of 0.04 inch. A random sample of 4 ​Ping-Pong balls is selected. What is the probability that the sample is between 1.26 and 1.3 ​inches?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The diameter of a brand of​ Ping-Pong balls is approximately normally​ distributed, with a mean of 1.31 inches and a standard deviation of 0.04 inch. A random sample of 4 ​Ping-Pong balls is selected. What is the probability that the sample is between 1.26 and 1.3 ​inches?
-----
z(1.26) = (1.26-1.31)/(0.04/sqrt(4)) = -0.05*2/0.04 = -0.10/0.04 = -2.5
z(1.3) = (1.3-1.31)/(0.04/sqrt(4)) = -0.01*2/0.04 = -0.02/0.04 = - 1/2
-----
P(1.26 < x-bar < 1.3) = p(-2.5 < z < -0.5) = normalcdf(-2.5,-0.5) = 0.3023
--------------
Cheers,
Stan H.
-----------