Question

The population mean and standard deviation are given below. Find the indicated probability and determine whether a sample mean in the given range below would be considered unusual. If convenient, use technology to find the probability For a sample of n 40, find the probability of a sample mean being less than 12.752 or greater than 12.756 when 12,752 and 1.5. For the given sample, the probability of a sample mean being less than 12,752 or greater than 12,755 is (Round to four decimal places as needed.) Would the given sample mean be considered unusual? O A. The sample mean would be considered unusual because there is a probability greater than 0.05 of the sample mean being within this range. O B. The sample mean would be considered unusual because there is a probability less than 0.05 of the sample mean being within this range. O C. The sample mean would not be considered unusual because there is a probability less than 0.05 of the sample mean being within this range. OD. The sample mean would not be considered unusual because there is a probability greater than 0.05 of the sample mean being within this range.

Answer 1

Solution Given that M: 12752 a:115 n = 40 PLEC 12752 od Ž 712755) The standard noomal using 2 T-M 12752 - 12752 1:5 Zo: 11 5 12755-12752 7.5 140 0.237171 =12.649101 Thus, Plzco.co od 2 712.649101) = Arca on left of 0.00 and on tight of 12.649101 PCSS 12752 or 712755)

= P(Z<0.00 8 27.12.649101) = P(z<0.00)+P(2712649101) - Plzco.00)+1- P(Z <12.649101) = 0.5+1-1 -015 Therefore The probability of a sample mean being less than 12752 od gocater than 12.755 is 0.5000) 90cater The gwen sample meant be considered unusual option @ is correct v . The sample mean would not be considered unusual because thede is a probability tess than 0.05 of the sample mean being with in songe This is not unusual, as the probability is quiet high