Given:
μ = 17.2 lb, the population mean
σ = 2.5 lb, the population standard deviation
The sample size is n = 55.
σ/√n =2.5/√55 = 3.0339
For the random variable x = 14 lb, with sample size = 55,
z = (x - μ)/(σ√n) = (14 - 17.2)/3.0339 = -1.0547
From standard tables, P(x<14) = 0.1458
For the random variable x = 18 lb,
z = (18 - 17.2)/3.0339 = 0.2637
P(x<18) = 0.604
Therefore
P(14 < x < 18) = 0.604 - 0.1458 = 0.4582
Answer: 0.458 or 45.8%
