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A standard quality check found that out of 200 light globes, 6 had a defect. (i) If the sample proportion is approximately normally distributed, show that the mean and sample standard deviation are 0.03 and 0.01206 respectively. (ii) Find the z-score if 4 light globes in this sample are defective. (iii) Use the section of the table showing the values of P(Z < z) to find the probability that the number of defective light globes in this sample was between 4 and 5.

A standard quality check found that out of 200 light globes, 6 had a defect. (i) If the sample proportion is approximately normally distributed, show that the mean and sample standard deviation are 0.03 and 0.01206 respectively. (ii) Find the z-score if 4 light globes in this sample are defective. (iii) Use the section of the table showing the values of P(Z < z) to find the probability that the number of defective light globes in this sample was between 4 and 5.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A standard quality check found that out of 200 light globes, 6 had a defect. (i) If the sample proportion is approximately normally distributed, show that the mean and sample standard deviation are 0.03 and 0.01206 respectively. Z 0.4 0.5 0.6 0.7 0.8 (ii) Find the z-score if 4 light globes in this sample are defective. (iii) Use the section of the table showing the values of P(Z <z) to find the probability that the number of defective light globes in this sample was between 4 and 5. 0.00 0.01 0.6554 0.6591 0.6628 0.6664 0.6700 0.6985 0.7019 0.6915 0.6950 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.6736 0.6772 0.6808 0.6844 0.6879 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.7389 0.7422 0.7454 0.7486 0.7518 0.7549 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7996 0.8023 0.8051 0.8079 0.8106 0.8133 0.7258 0.7291 0.7324 0.7357 0.7580 0.7612 0.7642 0.7673 0.7881 0.7910 0.7939 0.7967
Transcribed Image Text:A standard quality check found that out of 200 light globes, 6 had a defect. (i) If the sample proportion is approximately normally distributed, show that the mean and sample standard deviation are 0.03 and 0.01206 respectively. Z 0.4 0.5 0.6 0.7 0.8 (ii) Find the z-score if 4 light globes in this sample are defective. (iii) Use the section of the table showing the values of P(Z <z) to find the probability that the number of defective light globes in this sample was between 4 and 5. 0.00 0.01 0.6554 0.6591 0.6628 0.6664 0.6700 0.6985 0.7019 0.6915 0.6950 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.6736 0.6772 0.6808 0.6844 0.6879 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.7389 0.7422 0.7454 0.7486 0.7518 0.7549 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852 0.7996 0.8023 0.8051 0.8079 0.8106 0.8133 0.7258 0.7291 0.7324 0.7357 0.7580 0.7612 0.7642 0.7673 0.7881 0.7910 0.7939 0.7967
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