1) Scientists working for a water district measure the water level in a lake each day. The daily water level in the lake varies due to weather conditions and other factors, and has a distribution that is approximately normal with a mean water level of 84.07 feet. The probability that the daily water level in the lake is at least 100 feet is 0.064. (a) Show that the standard deviation is ? = 10.4803. (b) Find the probability that on a randomly selected day the water level in the lake will be at least 90 feet. (c) Find the 0.5th percentile; that is, find the value x* so that P(X < x*) = 0.005.
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