The number of contaminating particles on a silicon wafer prior to a certain rinsing process was determined for each wafer in a sample of size 100, resulting in the following frequencies: a. ?What proportion of the sampled wafers had at least one particle? At least five particles? b. ?What proportion of the sampled wafers had between five and ten particles, inclusive? Strictly between five and ten particles? c. ?Draw a histogram using relative frequency on the vertical axis. How would you describe the shape of the histogram?

Problem 19E Answer: Step1: We have The number of contaminating particles on a silicon wafer prior to a certain rinsing process was determined for each wafer in a sample of size 100, resulting in the following frequencies: Number of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Particles Frequency 1 2 3 12 11 15 18 10 12 4 5 3 1 2 1 We need to find, a. What proportion of the sampled wafers had at least one particle At least five particles b. What proportion of the sampled wafers had between five and ten particles, inclusive Strictly between five and ten particles c. Draw a histogram using relative frequency on the vertical axis. How would you describe the shape of the histogram Step2: a). Consider, Number of Particles Frequency 0 1 1 2 2 3 3 12 4 11 5 15 6 18 7 10 8 12 9 4 10 5 11 3 12 1 13 2 14 1 N = 100 (N F) 1).The proportion of the sampled wafers had at least one particle Ns = (1001) = 100 = 99/100 = 0.99 Therefore, 99% of the sampled wafers had at least one particle. 2).The proportion of the sampled wafers had at least five particle is = [100(1+2+3+12+11)] = 100 10029 = 100 = 71/100 = 0.71 Therefore, 71% of the sampled wafers had at least five particle. Step3: b). Consider, 5 15 6 18 7 10 8 12 9 4 10 5 64 1).Proportion of the sampled wafers had between five and ten particles is given by = 100 = 0.64 Therefore,64% of the sampled wafers had between five and ten particles. 2).Again consider, 6 18 7 10 8 12 9 4 44 Proportion of the sampled wafers had strictly between five and ten particles is given 100= = 0.44 Therefore,44% of the sampled wafers had strictly between five and ten particles. Step4: c). A histogram of given data is obtained by using Excel and steps are as follows •Enter the given data in Excel sheet. •select frequencies column go to insert choose histogram •then press ok. From the above histogram we can say that the given data is bell shaped hence the given data is normally distributed.