David is investing the amount of standard deviation in the time it takes a 3D printer to print a particular part of the car's engine. He believes that the standard deviation in the time to get the printing done is more than 2.5 . Test this at \( \alpha=0.01 \) level of significance using 15 samples times taken while the printer was doing its job. The sample standarc deviation is 3 .

Find the percentile of the data value. Data set: \( 3,13,10,6,3,3,13,6,3,13,2,13,15,4,9,3,12,10,6,13 \); data value: 6

Find the median. \( \begin{array}{l}0.88,1.18,0.64,1.62,0.75,0.85 \\ 1.18,1.53,0.91,0.88,1.39,1.07 \\ 0.47,1.39,0.85,1.07,1.72,0.75 \\ 1.12,0.89,0.56\end{array} \)

In order to monitor the ecological health of the Florida Everglades, various measurements are recorded at different times. The bottom temperatures are recorded at the Garfield Bight station and the mean of 30.4 C is obtained for 61 temperatures recorded on 61 different days. Assume a population standard deviation of 1.7 C , test the claim that the population mean is greater than 30.0 C . Use a 0.10 significance level. Decide whether to reject or fail to reject the null hypothesis and state your conclusion. You would [Select] [Select ] population mean is greater than 30.0 C .

A person's blood glucose level and diabetes are dosely related. Let \( x \) be a random variable measured in milligrams of glucose per deciliter ( \( 1 / 10 \) of a liter) of blood. Suppose that after a 12 -hoi fast, the random variable \( x \) will have a distribution that is approximately normal with mean \( \mu=87 \) and standard deviation \( \sigma=23 \). Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50 ) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) \( x \) is more than 60 (b) \( x \) is less than 110 (c) \( x \) is between 60 and 110 (d) \( x \) is greater than 125 (borderline diabetes starts at 125 )

The test scores of 40 students are listed below. Find \( \mathrm{P}_{85} \). \( \begin{array}{l}30,35,43,44,47,48,54,55,56,57,59,62,63,65,66,68,69,69,71,72,72,73, \\ 74,76,77,77,78,79,80,81,81,82,83,85,89,92,93,94,97,98\end{array} \)