More Normal Distribution Practice! Unit 2 Day 3 More Normal Distribution Practice!

Practice 1 On the driving range, Tiger Woods practices his swing with a particular club by hitting many, many balls. When Tiger hits his driver, the distance the ball travels follows a Normal distribution with mean 304 yards and standard deviation 8 yards. What percent of Tiger’s drives travel at least 290 yards?

STATE Express the problem in terms of the observed value x. Your answer should be similar to this: Let x = distance that Tiger’s ball travels. The variable x has a Normal distribution with μ = 304 and σ = 8. We want the proportion of Tiger’s drives with x ≥ 290.

PLAN Draw a picture of the distribution and shade the area of interest under the curve. Your answer should be similar to this:

DO Perform calculations. Your answer should be similar to this: Standardize x to restate the problem in terms of a standard Normal variable z. Use Table A and the fact that the total area under the curve is 1 to find the required area under the standard Normal curve Your answer should be similar to this: To standardize for x=290, we have So x ≥ 290 corresponds to z ≥ -1.75 under the standard Normal curve. Using Table A, we see that the proportion of observations less than -1.75 is 0.0401. About 4% of Tiger’s drives travel less than 290 yards. The area to the right of -1.75 is therefore 1 – 0.0401 = 0.9599. This is about 0.96, or 96%

CONCLUDE Write your conclusion in context of the problem. Your answer should be similar to this: About 96% of Tiger Wood’s drives on the range travel at least 290 yards.

Practice 2 What percent of Tiger’s drives travel between 305 and 325 yards? (State, Plan, Do, Conclude)