Question

Descripthe Statisties: Rating at bev 4,360 B Median Nean 94. 420 94,814 Varialle Rating 95.000 o1 9.000 174 Variable Minimum Maximum 4.000100.000 03 98.000 Rating 2 cruise ships arriving in the US are rated for sanitation on a scale of 100. The summa statistics for the rating of 174 cruise ships arriving in December 2017 are given in the table. a. Construct the interval which contains 95% of the observations and 99.7% of the ry observations. One of the ships has a rating of 74. Calculate the Z score for this observation and determine if it is an outlier. b.

Answer 1

Solution: a. Obtain the confidence interval Here, Mean 94.420, Sd 4300,n-174 Thus, the 95% confidence interval is, CI - Meanz Zoos Sd 4.300 94.4201.960x -114 = 94.420 ±0.6389 -(93.7811,95.0589) The 99.7% confidence interval is,

Sd CI = Mean±Z0003 4.300 = 94.420 ±2.968 ×174 94.420 ±0.9675 -934525,953875) Obtain the Z-score. The Z-score is, Z- score 74 94.420 4.3 -4.7488 The interquartile range is, - 98-92 Thus, the value 74 is lower than 92-1.5x IOR 83. Therefore, the value 74 is an outlier.