1. Text Exercise 1.30 (a) (b) (c) First, make a sketch representing this probability; then find the probability. 16 – 11 z = ——— = 1.43 3.5 0.1141 + 0.3729 = 0.4870 or 48.70% 0.5 – 0.4564 = 0.0436 or 4.36% Homework #3Score____________/ 10Name ______________

2. Text Exercise 1.32 (a) (b) First, make a sketch representing this probability; then find the probability. 0.5 – 0.1844 = 0.3156 or 31.56% 0.5 – 0.3106 = 0.1894 or 18.94%

3. Text Exercise 1.34 (a) (b) (c) First, make a sketch representing this probability; then find the probability. 0.0910 – 0.0714 = 0.0196 or 1.96% 0.3599 – 0.3485 = 0.0114 or 1.14% 0.3997 – 0.3907 = 0.0090 or 0.90%

4. Additional HW Exercise #1.6 (a) (b) 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. Playing times for cassette tapes manufactured by the Econo corporation are normally distributed with mean 46.4 minutes and standard deviation 2.5 minutes 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. 0.0478 or 4.78% 0.2358 or 23.58%

5. Additional HW Exercise #1.6 - continued (c) (d) 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. 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. 0.5646 or 56.46% 0.0638 or 6.38%

6. (e) (f) 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. 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. 0.8262 or 82.62% 0.8904 or 89.04%

7. Additional HW Exercise #1.6 - continued (g) (h) 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. 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. 0.7188 or 71.88% 0.0308 or 3.08%

8. (i) (j) 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. Should an Econo cassette tape with a playing time of 45 minutes be considered extremely unusual? Why or why not? practically 0 or 0% 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.

9. Additional HW Exercise #1.6 - continued (k) (l) 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? 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. 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.