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3.39. The tensile strength of a metal part is normally distributed with mean 40lb and standart deviation 5lb. If 50,000 parts are produced, how many would you expect to fail to meet a minimum specification limit of 35 lb tensile strength? How many would have a tensile strength in excess of 48 lb?3.40. The output voltage of a power supply is normally distributed with mean 5 V and standart deviation 0.02 V. If the lower and upper specifications for voltage are 4.95 V and 5.05 V, respectively, what is the probability that a power supply selected at random will conform to the specifications on voltage? 3.24. A manufacturer of electronic calculators offers a one-year warranty. If the calculator fails for any reason during this period, it is replaced. The time to failure is well modeled by the following probability distribution:fx=0.125e-0.125x x>0a) What percentage of the calculators will fail within the warranty period ?b) The manufacturing cost of a calculator is $50, and the profit per sale is $25. What is the effect of warranty replacement on profit ?3.24.(a)This is an exponential distribution with parameter λ = 0.125:Pr{x ≤1} = F(1) =1? e?0.125(1) = 0.118Approximately 11.8% will fail during the first year.(b)Mfg. cost = $50/calculatorSale profit = $25/calculatorNet profit = $[-50(1 + 0.118) + 75]/calculator = $19.10/calculator.The effect of warranty replacements is to decrease profit by $5.90/calculator.4.1. The diameters of aluminum alloy rods produced on an extrusion machine are known to have a standard deviation of 0.0001 in. A random sample of?25 rods has an average diameter of 0.5046 in.?a) Test the hypothesis that mean rod diameter is 0.5025 in. Assume a?two-sided alternative and use α= 0,05b) Find the P-value for this test.?c) Construct a two-sided 95% confidence interval on the mean rod diameter.α = 0.05 σ =4 lb Confidence interval width = 1 lbtwo-sided confidence interval width = 1 = 1 = n =2465.23. Consider the time-varying process behaviour shown below. Match each of these several patterns of process performance to the corresponding x and R charts shown in figures (a) to (e) below ?Question : Apply the Western electric rules to the control charts presented below. Would these rules result in any out of control signal ?Xbar - chartR-chartChecking for out of control conditions we have the following 8 tests:Test 1 : Extreme points -> points 8, 20, 32, 44 on x bar chart & no extreme points on R chart.Test 2: Two out of Three Points in or beyond Zone A -> 20, 21Test 3: Four out of Five Points in or beyond Zone B -> 25, 26, 27Test 4: Runs Above or Below the Centerline (Eight or more consecutive points) -> No points satisfying this condition both on x bar and R charts.Test 5: Linear Trend Identification (Six or more consecutive points) -> 25, 26Test 6: Oscillatory Trend Identification( 14 or more consecutive points) -> No pointsTest 7: Avoidance of Zone C (8 or more consecutive points) -> No pointsTest 8: Run in Zone C (15 or more consecutive points) -> No pointsWe check for all of the 8 tests above for x bar chart. However for R chart, we don’t apply tests that contain zones (tests 2,3,7 and 8), thus they are not needed to be checked. (Only 1,4,5,6 th tests should be checked for an R chart)
What is the antilog of 2.0440228?
