Consider the sample of exam scores to the right, arranged in increasing order. The sample mean and sample standard deviation of these exam scores aro, respectively, 83.0 and 177. Chebycher's rule states that for any data set and any real number k>1, at least 100(1-1/K?)% of the observations lio 25 44 52 59 60 74
within k standard deviations to other side of the mean Complete parts (a) and (b) below.
81 81 82 85 85 85
87 90 90 90 91 92
92 92 93 93 94 94
94 95 96 96 98 100
a. Use Chebychev's rule to obtain a lower bound on the percentage of observations that lie within three standard deviations to either side of the mean.
(Round to one decimal place as needed)

Which expression is equivalent to? assume x > 0 and y > 0.

Thanh and her crew are building a stage in the shape of a trapezoid for an upcoming festival. the lengths of the parallel sides of the trapezoid are 14 ft and 24 ft. the height of the trapezoid is 12 ft.what is the area of the stage? enter your answer in the box. ft²

Atechnician compares repair costs for two types of microwave ovens (type i and type ii). he believes that the repair cost for type i ovens is greater than the repair cost for type ii ovens. a sample of 6767 type i ovens has a mean repair cost of $79.79$⁢79.79. the population standard deviation for the repair of type i ovens is known to be $19.18$⁢19.18. a sample of 5555 type ii ovens has a mean repair cost of $75.24$⁢75.24. the population standard deviation for the repair of type ii ovens is known to be $21.40$⁢21.40. conduct a hypothesis test of the technician's claim at the 0.050.05 level of significance. let μ1μ1 be the true mean repair cost for type i ovens and μ2μ2 be the true mean repair cost for type ii ovens. step 2 of 4 : compute the value of the test statistic. round your answer to two decimal places.