Below are tabulated a number of Rockwell G hardness values that were measured on a single steel specimen. Compute (a) the average hardness value and (b) the standard deviation hardness value. 50.5 48.8 48.9 47.1 46.9 46.5 46.6 47.7 48.4 49.7 50.1 50.4   (a)      (b)

A drug company claims that their products’ contaminations never vary by more than 2%. Sample of 5 specimens were tested and the percentages of the purities are recorded as Observation no. 1 2 3 4 5 Percentages (%) 98.8 97.2 98.9 97.7 97.9 a. Do the sample data have enough proof to oppose the manufacturer's claim? (HINT: take the range of 2% equal 4o.) b. Find a 90% confidence interval for o?.

The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean u, the actual temperature of the medium, and standard deviation o. n USE SALT What would the value of o have to be to ensure that 95% of all readings are within 0.8° of µ? (Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.72. (c) How large a sample size is necessary if the width of the 95% interval is to be 0.45? (Round your answer up to the nearest whole number.)  ................ specimens(d) What sample size is necessary to estimate true average porosity to within 0.24 with 99% confidence? (Round your answer up to the nearest whole number.) ................. specimens