Part 2: a) Your Manufacturing Division produces capacitors with a nominal value of 47 µF, with a tolerance of +/- 10%. A random sample of ten capacitors was taken, and their value was measured by a colleague, to check that they remain within tolerance. The results are as follows: Sample Capacitance (µF) 1 2 3 4 5 6 7 8 9 10 51 46 43 46 51 51 46 48 49 47 (i) Calculate the mean capacitance for these samples. (ii) Determine the standard deviation for the samples. (iii) Produce a Tally Chart showing the frequency of measured capacitances. b) Further analysis of a larger sample of the capacitors shows that 85% are within the allowable tolerance value. The remainder exceed the tolerance. You select eight capacitors at random from the sample. Determine the probabilities that: (i) Two of the eight capacitors exceed the tolerance. (ii) More than two of the eight capacitors exceed the tolerance.
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To calculate the mean capacitance, we need to sum up all the measured capacitances and divide by the number of samples. Sum of capacitances = 51 + 46 + 43 + 46 + 51 + 51 + 46 + 48 + 49 + 47 = 480 Mean capacitance = Sum of capacitances / Number of samples = 480 / Show more…
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David N.
1) A batch of 100 capacitors contains 73 which are within the required tolerance values, 17 which are below the required tolerance values, and the remainder are above the required tolerance values. Determine the probabilities that when randomly selecting a capacitor and then a second capacitor: (a) both are within the required tolerance values when selecting with replacement, and (b) the first one drawn is below and the second one drawn is above the required tolerance value, when selection is without replacement. 2) In a batch of 45 lamps there are 10 faulty lamps. If one lamp is drawn at random, find the probability of it being (a) faulty and (b) satisfactory. 3) A box of fuses are all of the same shape and size and comprises 23 2A fuses, 47 5A fuses and 69 13A fuses. Determine the probability of selecting at random (a) a 2A fuse, (b) a 5A fuse and (c) a 13A fuse.
Sree R.
A type of capacitor has resistances that vary according to a normal distribution with a mean of 800 megohms and a standard deviation of 200 megohms. A certain application specifies capacitor with resistance between 900 and 1,000 megohms. (a) What proportion of these capacitors will meet the specification? (b) What must be the standard deviation of the resistance so that the 35% of the capacitors will be suitable for the application if it the process was centered with mean equal to 9500 megohms? (c) If three capacitors are randomly chosen from a lot of capacitors, what is the probability that all three will satisfy the specification? (d) If a new capacitor from a different company was used with a mean value of 880 megohms with the same standard deviation, what proportion of the new capacitor will meet this specification?
Sri K.
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