Question

6. (10 points) A zoologist collected wild lizards in the Southwestern United States. Thirty lizards from the genus Phrynosoma were placed on a treadmill and their speed measured. The recorded speed (meters/second) is the fastest time to run a half meter. 1.28 1.36 1.24 2.47 1.94 2.52 2.67 1.29 1.56 2.66 2.17 1.57 2.10 2.54 1.63 2.11 2.57 1.72 0.76 1.02 1.78 0.50 1.49 1.57 .04 1.92 1.55 1.78 1.70 1.20 a. Find the sample median, first quartile, and third quartile b. Find the sample 90th percentile. c. Calculate r and s d. Find the proportion of the observations that are in each of the intervals s, 2s, 3s 7. (5 points) The city of Madison regularly checks the water quality at swimming beaches located on area lakes. In fifteen measurements, the concentration of fecal coliforms, in number of Colony Forming Units (CFU) per 100 ml of water, was found during the summer at one beach. 180 1600 90 140 50 260 400 90 380 110 10 60 20 340 80 a. Calculate the sample variance. b. Calculate the sample standard deviation c. One day, the water quality was bad. The reading was 1600 CFU, and the beach was closed. Drop this value and calculate the sample standard deviation for the days where the water quality was suitable for swimming Comment on the change.

Answer 1

6.(a) sample median = 1.665, first quartile = 1.308, third quartile = 2.107.
(b) sample 90th percentile = 2.543.
(c) mean = 1.724, s = 0.573.
(d) Proportion of observations within $\bar{x} \pm s$ = 20/30 = 0.667.
Proportion of observations within $\bar{x} \pm 2s$ = 29/30 = 0.967.
Proportion of observations within $\bar{x} \pm 3s$ = 30/30 = 1.000.