Question

This Question: 3 pts 7 of 11 (0 complete) This Quiz: 17 pts possible Question Help The overhead reach distances of adult females are normally distributed with a mean of 200 cm and a standard deviation of 8.9 cm. a. Find the probability that an individual distance is greater than 209.30 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 198.50 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is a (Round to four decimal places as needed.) b. The probability is (Round to four decimal places as needed.) c. Choose the correct answer below. O A. The normal distribution can be used because the mean is large. OB. The normal distribution can be used because the original population has a normal distribution O c. The normal distribution can be used because the probability is less than 0.5 OD. The normal distribution can be used because the finite population correction factor is small

Answer 1

det Xi denotes the overhead reach distance if adwr Pernales. Then ie 1 (1) 200 Xin Nl 200,(8.912) => xi NN (200, 79121) a) Prob of an individucil's distance pl xy 209.30) is them 209.30 cm. grecites 209.3 - 200 p( x-2007 8.91 89 - 1 - Z 9.3 8.4 pl = 1- pl 2C 1.04) 1- 0.85 - 0.15 0:15 :. The required prob is b) het ", "2.. Yis be the 15 random sample. Ỹc ( 200, 79;2') Ý N ( 20 0, 5:28) P ( mean for 15 randomly selected distance is greater them 198.50 cm) Þ ( Ý > 198.50) 1 198.50-200 pl Y-200 √5.28 5:28 z y . pl 0.65) = 1- pl za - 0.65) £ (0.65) 1 + = 0.74 2. The required prob is 0.74. CS

c. Choose the correct option B) The normal distribution can be used because the original population has a normal distribution. CS Scanned with CamScanner