7.19 (a) Because the population diameter of Ping-Pong balls is approximately normally
distributed, the sampling distribution of samples of 16 will also be approximately
normal.
(b) P( X < 1.28) = P(Z < – 2.00) = 0.0228
(c) P(1.31 < X < 1.33) = P(1.00 < Z < 3.00) = 0.99865 – 0.8413 = 0.1574
(d) P(A < X < B) = P( −0.84 < Z < 0.84) = 0.60
Lower bound: X = 1.30 – 0.84(0.01) = 1.2916
Upper bound: X = 1.30 + 0.84(0.01) = 1.3084
(d) With the sample size increasing from n = 25 to n = 100, more sample means will be
closer to the distribution mean. The standard error of the sampling distribution of size
100 is much smaller than that of size 25, so the likelihood that the sample mean will
fall within 0.2 minutes of the mean is much higher for samples of size 100
(probability = 0.6826) than for samples of size 25 (probability = 0. 3830).