Homework 3 Score 10 Name Text Exercise 1

Homework #3 Score______ / 10 Name _______ Text Exercise 1. 30 (a) 16 – 11 z = ——— = 1. 43 3. 5 (b) First, make a sketch representing this probability; then find the probability. 0. 1141 + 0. 3729 = 0. 4870 or 48. 70% (c) First, make a sketch representing this probability; then find the probability. 0. 5 – 0. 4564 = 0. 0436 or 4. 36%

Text Exercise 1. 32 (a) First, make a sketch representing this probability; then find the probability. 0. 5 – 0. 1844 = 0. 3156 or 31. 56% (b) First, make a sketch representing this probability; then find the probability. 0. 5 – 0. 3106 = 0. 1894 or 18. 94%

Text Exercise 1. 34 (a) First, make a sketch representing this probability; then find the probability. 0. 0910 – 0. 0714 = 0. 0196 or 1. 96% (b) First, make a sketch representing this probability; then find the probability. 0. 3599 – 0. 3485 = 0. 0114 or 1. 14% (c) First, make a sketch representing this probability; then find the probability. 0. 3997 – 0. 3907 = 0. 0090 or 0. 90%

Additional HW Exercise #1. 6 Playing times for cassette tapes manufactured by the Econo corporation are normally distributed with mean 46. 4 minutes and standard deviation 2. 5 minutes (a) Draw a sketch illustrating the probability that one randomly selected Econo cassette tape has a playing time within 0. 15 minutes of the population mean, and find this probability. 0. 0478 or 4. 78% (b) Draw a sketch illustrating the probability that the mean playing time for a simple random sample of 25 Econo cassette tapes is within 0. 15 minutes of the population mean, and find this probability. 0. 2358 or 23. 58%

Additional HW Exercise #1. 6 - continued (c) Draw a sketch illustrating the probability that the mean playing time for a simple random sample of 169 Econo cassette tapes is within 0. 15 minutes of the population mean, and find this probability. 0. 5646 or 56. 46% (d) Draw a sketch illustrating the probability that one randomly selected Econo cassette tape has a playing time within 0. 2 minutes of the population mean, and find this probability. 0. 0638 or 6. 38%

(e) Draw a sketch illustrating the probability that the mean playing time for a simple random sample of 289 Econo cassette tapes is within 0. 2 minutes of the population mean, and find this probability. 0. 8262 or 82. 62% (f) Draw a sketch illustrating the probability that the mean playing time for a simple random sample of 400 Econo cassette tapes is within 0. 2 minutes of the population mean, and find this probability. 0. 8904 or 89. 04%

Additional HW Exercise #1. 6 - continued (g) Draw a sketch illustrating the probability that one randomly selected Econo cassette tape has a playing time more than 0. 9 minutes away from (below or above) the population mean, and find this probability. 0. 7188 or 71. 88% (h) Draw a sketch illustrating the probability that the mean playing time for a simple random sample of 36 Econo cassette tapes is more than 0. 9 minutes away from (below or above) the population mean, and find this probability. 0. 0308 or 3. 08%

(i) Draw a sketch illustrating the probability that the mean playing time for a simple random sample of 100 Econo cassette tapes is more than 0. 9 minutes away from (below or above) the population mean, and find this probability. practically 0 or 0% (j) Should an Econo cassette tape with a playing time of 45 minutes be considered extremely unusual? Why or why not? Since 28. 77% of all Econo cassette tapes have a playing time of less than 45 minutes, we cannot consider a cassette tape with a playing time of 45 minutes unusual.

Additional HW Exercise #1. 6 - continued (k) Should a simple random sample of 4 Econo cassette tapes with a mean playing time of 45 minutes be considered extremely unusual? Why or why not? Since 13. 14% of all samples of size n = 4 cassette tapes have a mean playing time less than 45 minutes, we cannot consider a sample of size n = 4 with mean 45 minutes unusual. (l) Should a simple random sample of 100 Econo cassette tapes with a mean playing time of 45 minutes be considered extremely unusual? Why or why not? Since practically no samples of size n = 100 cassette tapes have a mean playing time less than 45 minutes, we can consider a sample of size n = 100 with mean 45 minutes very unusual.