The output of a power supply is assumed to be normally distributed. 16 observations taken at random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 9.25, 9.38 and 10.85. (a) Test the hypothesis that the mean voltage equals 12V against a two-sided alternative using α=0.05. (b)Construct a 95% confidence interval on µ. (c) Test the hypothesis that σ2 =1 using α=0.05. (d)Construct a 95% two-sided confidence interval on σ. (e) Construct a 95% upper confidences interval on σ.

Afoot bridge is made as a simple deck, 4 m long, with a cross section 2 m (wide) and 20 cm thick, and made of wood. the deck is supported at the two ends. the maximum load allowable on the bridge is 10 tons, provided it is uniformly distributed on the deck. to sense this load, a strain gauge is placed at the center of the bridge and its resistance is monitored. if the sensor has a nominal resistance of 350 s2 and a gauge factor of 3.6, what is the reading of the strain gauge at maximum load? the modulus of elasticity for the wood used in the construction is 10 gpa.