Question

5. A stamping process makes steel washers with a 2 inch outer diameter, 1.062 inch inner diameter, and a variable thickness of 0.118 to 0.132 inches. A particular lot of washers in found to have a mean thickness of 0.1250 inches, with a standard deviation of 0.0035 inches. Assuming the production follows a normal distribution and using the z-table provided and rounding appropriately determine: Figure 1: Amage from McMaster a. The probability that a washer have a thickness less than 0.132 Carr, 316 Stainless Steel Washer inches. b. The probability that a washer with have a thickness less than 0.115 inches. C. At cost, the washers have a value of $0.02 each. If all washers greater than 0.132 inches thick or thinner than 0.118 inches must be discarded. How much money is lost for a run of 10,000 washers? Note - for each portion label the mean as given, the point of interest, and shade the area you are looking for Final Answers

Answer 1

NOTE

$Probability\: \: Factor (z) = \frac{x-\overline{x}}{\sigma }$

where,

• x = Given value
• $\overline{x}$ = Mean Value
• $\sigma$ = Standard Deviation

DETAILED SOLUTION

mean thickness , n = 0.125 in Standard deviation, - = 0.0035 in probability factor (z) = *-*| (a) Poobability that a washer have a less than 0.132 in thickness N=0.132 in ñ= 0.125 in r = 0.0035 in _0.132-0.125 0.0035 [z=2 [P(222) = 0.97725 o probability that a washer have a thickness less than 0.132 in = 97.725% with have a thickness (6) Probability that a washer less than 0.115 in n=0.115 ñ=0.125 16 = 0.0035 Z-0.115 -0.125 0.0035 Z= -2.8571 PC2< -2.857) = 2.1384 x 10-3 7 PC25-2.857) = 0.214 % -2.857

=> Probability that a washer with thickness less than 0.115 in = 0.214 % Ecost for a single washer = $0.02 -> cost for 10,000 washers = 10000 $0.02 = 1200$ -> probabity of casher with thickness greater 0.132 in = 1 - Probability of Washer with thickness less than 0.132 in ♡ Poobality of Washer with thickness less than 0-132 in = 97.725% {from question as -> probabity of washes with thickness greater than 0.132 in = 100 – 97,725 = 2.275 % probability of washer with thickness less than 0.118 in. N =0118 in ł=0.125 in Z -0.118-0:125 a = 0.0035 in 0.0035 [z = -2 PC24 - 2) = 0.02275 (P(Z <-2) = 2.275% TI -a

-> Summing up the probabilities of washers to be discarded = 2.275% +2.275 % = 14.55% -> 4.55% of Total money spent is lost. = 4:55 x 200 Too ^ 200 = 9.1$ (Money lost due to discarded washers = $9.1)

FINAL ANSWERS

(a) The probability that a washer has a thickness of less than 0.132 in = 97.725 %

(b) The probability that a washer has a thickness of less than 0.115 in = 0.214 %

(c) Money lost due to Discarded washers = 9.1 $