Question

[A] From 21, 27, 46, 35, 41, 36, 25 Find (1) Median, (2) Mean, (3) Standard Deviation [B] Only 65% of the mountain climber who tried, reach the top of the High-top mountain during last 10 years. In a random sample of 11 mountain climbers who had tried, find the following information (4) the probability of at least 9 reached the top (5) the expected value (6) the standard deviation [C] The length of time to make a device is normally distributed with mean = 6.7 minute and standard deviation=2.2 minute. At random, (7) what is the probability of the time will be at least 10 minutes (8) if 16 devices are selected at random, what is the probability that their average is no more than 5 minutes? (D) (9) A random sample of 19 fish caught at a lake, the sample mean length=11.9" with a sample standard deviation=2.8". Find the 99% confidence interval for the population mean length of all the fish at the lake.

Answer 1

21, 27, 46, 35, 41, 36,25 1) median I role, assange in ascending 21,25, 27, 35, 36, 41, 46 Median - 35 = 33 2) mean = 21+25+27+35+3 6+41 +46 2 3 4 7 7 3) S.D 6 ħ u cai-u? (21-33)2 + (25-33² + 27-33/² + (35-33) +- € +- €46-3372 6 Lugo [B] 4) Probability of at least I reached the top- 60-6590 6-353 +1cie (0-65)) (035) + 11c,, (0.65)" leg 0.200 128857 5). expected value np n=11, p=0.65 = 7.15 6) SAD s = unpa Slix0.65 0.35 2.5025

u= 6,7 minute meant S.D = 2.2 minule P ( X = 10) 7) z = xy P (27, 10-6.7 2.2 0.0 668 Plz>, los) = If 16 devices are selected at radon rendom central limit theorem using normal distribution follow so sample mean X with mean u = 6.7 6155 212 = 0.55 6 New - 2.2 16 P (X<5) 2= x - 6.7 0.55 P (x=-1-7) 0.ooo997 P 1X<-3.09090go) = Ams