Question

The diameter of Ping-Pong balls manufactured at a large factory is expected to be approximately normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inches. What is the probability that a randomly selected Ping-Pong ball will have a diameter of:

a. Between 1.28 and 1.30 inches?
b. Between 1.31 and 1.33 inches?
c. Between what two values will 60% of the Ping-Pong balls fall (in terms of the diameter)?
If random samples of 16 Ping-Pong balls were selected,
d. What proportion of the sample means would be between 1.31 and 1.33 inches?
If random samples of 100 Ping-Pong balls were selected,
e. What proportion of the sample means would be between 1.31 and 1.33 inches?

f. Compare your results in (b), (d) and (e).

Answer 1

The diameter of Ping-Pong balls manufactured at a large factory is expected to be approximately normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inches. --- If you don't have software or a calculator you will have to do these using z-values and a z-chart. My answers are based on using a TI calculator. ----------- What is the probability that a randomly selected Ping-Pong ball will have a diameter of: a. Between 1.28 and 1.30 inches? Ans: normalcdf(1.28,1.30,1.30,0.04) = 0.1915 -------------------------------------- b. Between 1.31 and 1.33 inches? Ans: normalcdf(1.31,1.33,1.30,0.04) = 0.1747 -------------------------------------- c. Between what two values will 60% of the Ping-Pong balls fall (in terms of the diameter)? You need the z-value that is 30% to the right and 30% to the left of the mean. That value is InvNorm(0.20) = 0.8416 Then you have to use x = u + z*sugma to find the correct x-values ------------------------------------------ If random samples of 16 Ping-Pong balls were selected, d. What proportion of the sample means would be between 1.31 and 1.33 inches? If random samples of 100 Ping-Pong balls were selected, --- The standard deviation has changed to 0.04/sqrt(16) = 0.01 because of the Central Limit Theorem. Ans: normalcdf(1.31,1.33,1.3,0.01) = 0.1573 ------------------------------------------------------ I'll leave the rest to you. Cheers, Stan H. =========================================== e. What proportion of the sample means would be between 1.31 and 1.33 inches? f. Compare your results in (b), (d) and (e).