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5. In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 29. a) If 10 000 cookies were produced, how many cookies are within 2 g of the mean? b) Cookies are rejected if they weigh more than 44 g or less than 36 g. How many cookies would you expect to be rejected in a sample of 10 000 cookies? 6. The speeds of cars on the highway have a mean of 95 km/h with a standard deviation of 5 km/h. a) What percentoge of cars averaged less than 85 km/h? b) If a police car stopped cars that were going more than 105 km/h, how many cars would they stop if there were 8000 cars on the highway?

5. In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 29. a) If 10 000 cookies were produced, how many cookies are within 2 g of the mean? b) Cookies are rejected if they weigh more than 44 g or less than 36 g. How many cookies would you expect to be rejected in a sample of 10 000 cookies? 6. The speeds of cars on the highway have a mean of 95 km/h with a standard deviation of 5 km/h. a) What percentoge of cars averaged less than 85 km/h? b) If a police car stopped cars that were going more than 105 km/h, how many cars would they stop if there were 8000 cars on the highway?

MATLAB: An Introduction with Applications
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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Do number 5 and 6. This is not graded.
Essential Statistics Worksheet on Normal Distribution Name: For each question, construct a normal distribution curve and label the horizontal axis. Then answer each question. 1. The mean life of a tire is 30 000 km. The standard deviation is 2000 km. a) 68% of all tires will have a life between b) 95% of all tires will have a life between _km and km. c) What percent of the tires will have a life that exceeds 26 000 km? d) If a company purchased 2000 tires, how many tires would you expect to last more than 28 000 km? km and km. 2. The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. a) About what percent of the products last between 9 and 15 days? b) About what percent of the products last between 12 and 15 days? c) About what percent of the products last 6 days or less? d) About what percent of the products last 15 or more days? 3. A line up for tickets to a local concert had an average (mean) waiting time of 20 minutes with a standard deviation of 4 minutes. a) What percentage of the people in line waited for more than 28 minutes? b) If 2000 ticket buyers were in line, how many of them would expect to wait for less than 16 minutes? 4. On a recent math test, the mean score was 75 and the standard deviation was 5. Mike made 93. Would his mark be considered an outlier if the marks were normally distributed? Explain. 5. In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 2 9. a) If 10 000 cookies were produced, how many cookies are within 2 g of the mean? b) Cookies are rejected if they weigh more than 44 g or less than 36 g. How many cookies would you expect to be rejected in a sample of 10 000 cookies? 6. The speeds of cars on the highway have a mean of 95 km/h with a standard deviation of 5 km/h. a) What percentage of cars averaged less than 85 km/h? b) If a police car stopped cars that were going more than 105 km/h, how many cars would they stop if there were 8000 cars on the highway? 7. The Floppy Disk Company makes 3.5 inch floppy disks for disk drives that are 3.7 inches wide. The size of a manufactures disk is normally distributed with a standard deviation of 0.1 inches. The company manufactures 1000 disks every hour. a) What % of the disks would you expect to be greater than 3.5 inches? b) In one hour, how many disks would you expect to be between 3.4 inches and 3.7 inches? c) About how many disks will be unable to fit in the disk drive (3.7 inch won't fit)? 8. The mean life of a battery is 50 hours with a standard deviation of 6 hours. The manufacturer advertises that they will replace all batteries that last less than 38hours. If 50 000 batteries were produced, how many would they expect to replace? 9. A bottle of fruit punch contains at least 473 ml. The machine that fills the bottles is set so that the mean volume is 477 ml. The volumes in the bottles are normally distributed. a) What percent of the bottles are underfilled if the standard deviation is 2 ml? b) What percent of the bottles are underfilled if the standard deviation is 4 ml? 10. A grading scale is set up for 1000 students' test scores. It is assumed that the scores are normally distributed with a mean score of 75.ond a standerd devintinn af 15 a) How many students will have scores between 45 and 757
Transcribed Image Text:Essential Statistics Worksheet on Normal Distribution Name: For each question, construct a normal distribution curve and label the horizontal axis. Then answer each question. 1. The mean life of a tire is 30 000 km. The standard deviation is 2000 km. a) 68% of all tires will have a life between b) 95% of all tires will have a life between _km and km. c) What percent of the tires will have a life that exceeds 26 000 km? d) If a company purchased 2000 tires, how many tires would you expect to last more than 28 000 km? km and km. 2. The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. a) About what percent of the products last between 9 and 15 days? b) About what percent of the products last between 12 and 15 days? c) About what percent of the products last 6 days or less? d) About what percent of the products last 15 or more days? 3. A line up for tickets to a local concert had an average (mean) waiting time of 20 minutes with a standard deviation of 4 minutes. a) What percentage of the people in line waited for more than 28 minutes? b) If 2000 ticket buyers were in line, how many of them would expect to wait for less than 16 minutes? 4. On a recent math test, the mean score was 75 and the standard deviation was 5. Mike made 93. Would his mark be considered an outlier if the marks were normally distributed? Explain. 5. In an Oreo factory, the mean mass of a cookie is given as 40 g. For quality control, the standard deviation is 2 9. a) If 10 000 cookies were produced, how many cookies are within 2 g of the mean? b) Cookies are rejected if they weigh more than 44 g or less than 36 g. How many cookies would you expect to be rejected in a sample of 10 000 cookies? 6. The speeds of cars on the highway have a mean of 95 km/h with a standard deviation of 5 km/h. a) What percentage of cars averaged less than 85 km/h? b) If a police car stopped cars that were going more than 105 km/h, how many cars would they stop if there were 8000 cars on the highway? 7. The Floppy Disk Company makes 3.5 inch floppy disks for disk drives that are 3.7 inches wide. The size of a manufactures disk is normally distributed with a standard deviation of 0.1 inches. The company manufactures 1000 disks every hour. a) What % of the disks would you expect to be greater than 3.5 inches? b) In one hour, how many disks would you expect to be between 3.4 inches and 3.7 inches? c) About how many disks will be unable to fit in the disk drive (3.7 inch won't fit)? 8. The mean life of a battery is 50 hours with a standard deviation of 6 hours. The manufacturer advertises that they will replace all batteries that last less than 38hours. If 50 000 batteries were produced, how many would they expect to replace? 9. A bottle of fruit punch contains at least 473 ml. The machine that fills the bottles is set so that the mean volume is 477 ml. The volumes in the bottles are normally distributed. a) What percent of the bottles are underfilled if the standard deviation is 2 ml? b) What percent of the bottles are underfilled if the standard deviation is 4 ml? 10. A grading scale is set up for 1000 students' test scores. It is assumed that the scores are normally distributed with a mean score of 75.ond a standerd devintinn af 15 a) How many students will have scores between 45 and 757
Expert Solution
Step 1

Assume, X be the random variable which follows normal distribution with Mean=μ and Standard deviation=σ.  

The proportion or percentage of data points with value in between a and b, can be given by the area under the normal distribution curve (with Mean=μ and Standard deviation=σ) that lies between X=a and X=b.

The normal curve is a bell shaped curve which is symmetric about mean.

The empirical rule states that for bell shaped distribution, 68% of data lies within 1 standard deviation from mean, 95% of data lies within 2 standard deviation from mean,  and 99.7% of data lies within 3 standard deviation from mean.

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