A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed. Find a 99% conﬁdence interval for the mean yield when the new catalyst is used.Q1: 12 (Exercise for Section 5.2)In a random sample of 150 customers of a high-speed internet provider, 63 said that their service had been interrupted one or more times in the past month.Find a 95% conﬁdence interval for the proportion of customers whose service was interrupted one or more times in the past month.Find a 99% conﬁdence interval for the proportion of customers whose service was interrupted one or more times in the past month.Find the sample size needed for a 95% conﬁdence interval to specify the proportion to within ± 0.05Find the sample size needed for a 99% conﬁdence interval to specify the proportion to within±0.05.Do bathroom scales tend to underestimate a person’s true weight? A 150 lb test weight was placed on each of 50 bathrooms scales. The readings on 29 of the scales were too light, and the readings on the other 21 were too heavy. Can you conclude that more than half of bathroom scales underestimate weight?A broth used to manufacture a pharmaceutical product has its sugar contents, in mg/mL ,measured several times on each of three successive days.Day 1: 5.0 4.8 5.1 5.1 4.8 5.1 4.8 4.8 5.0 5.2 4.9 4.9 5.0 Day 2: 5.8 4.7 4.7 4.9 5.1 4.9 5.4 5.3 5.3 4.8 5.7 5.1 5.7Day 3: 6.3 4.7 5.1 5.9 5.1 5.9 4.7 6.0 5.3 4.9 5.7 5.3 5.6Can you conclude that the variability of the process is greater on the second day than on the ﬁrst day?Can you conclude that the variability of the process is greater on the third day than on the second day?Mom and Grandma are each baking chocolate chip cookies. Each gives you two cookies. One of Mom’s cookies has 14 chips in it and the other has 11. Grandma’s cookies have 6 and 8 chips.Estimate the mean number of chips in one of Mom’s cookies.Estimate the mean number of chips in one of Grandma’s cookies.Find the uncertainty in the estimate for Mom’s cookies.Find the uncertainty in the estimate for Grandma’s cookies.Estimate how many more chips there are on the average in one of Mom’s cookies than in one of Grandma’s. Find the uncertainty in this estimate.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed. Find a 99% conﬁdence interval for the mean yield when the new catalyst is used.
Q1: 12 (Exercise for Section 5.2)
1. In a random sample of 150 customers of a high-speed internet provider, 63 said that their service had been interrupted one or more times in the past month.
2. Find a 95% conﬁdence interval for the proportion of customers whose service was interrupted one or more times in the past month.
3. Find a 99% conﬁdence interval for the proportion of customers whose service was interrupted one or more times in the past month.
4. Find the sample size needed for a 95% conﬁdence interval to specify the proportion to within ± 0.05
5. Find the sample size needed for a 99% conﬁdence interval to specify the proportion to within±0.05.
Do bathroom scales tend to underestimate a person’s true weight? A 150 lb test weight was placed on each of 50 bathrooms scales. The readings on 29 of the scales were too light, and the readings on the other 21 were too heavy. Can you conclude that more than half of bathroom scales underestimate weight?
1. A broth used to manufacture a pharmaceutical product has its sugar contents, in mg/mL ,measured several times on each of three successive days.
Day 1: 5.0 4.8 5.1 5.1 4.8 5.1 4.8 4.8 5.0 5.2 4.9 4.9 5.0

Day 2: 5.8 4.7 4.7 4.9 5.1 4.9 5.4 5.3 5.3 4.8 5.7 5.1 5.7

Day 3: 6.3 4.7 5.1 5.9 5.1 5.9 4.7 6.0 5.3 4.9 5.7 5.3 5.6
1. Can you conclude that the variability of the process is greater on the second day than on the ﬁrst day?
2. Can you conclude that the variability of the process is greater on the third day than on the second day?
Mom and Grandma are each baking chocolate chip cookies. Each gives you two cookies. One of Mom’s cookies has 14 chips in it and the other has 11. Grandma’s cookies have 6 and 8 chips.
Estimate the mean number of chips in one of Mom’s cookies.
Estimate the mean number of chips in one of Grandma’s cookies.
Find the uncertainty in the estimate for Mom’s cookies.
Find the uncertainty in the estimate for Grandma’s cookies.
Estimate how many more chips there are on the average in one of Mom’s cookies than in one of Grandma’s. Find the uncertainty in this estimate.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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