Advanced Math Topics 7 4 Applications of the

Advanced Math Topics 7. 4 Applications of the Normal Curve

1) A tire company has a reputation that their tires last an average of 28, 000 miles with a standard deviation of 4, 000 miles. What percentage of the tires are expected to last more than 35, 000 miles? z = x - μ = 35, 000 – 28, 000 = 1. 75 σ 4, 000. 5000 -. 4599 =. 0401 4. 01% of the tires can be expected to last more than 35, 000 miles. z 0. 00 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06 0. 07 0. 08 0. 09 - - - 1. 7 0. 4554 0. 4564 0. 4573 0. 4582 0. 4591 0. 4599 0. 4608 0. 4616 0. 4625 0. 4633

2) A TV company found that a TV tube is normally distributed with a standard deviation of 1. 53 years. If 7% of these tubes last more than 6. 9944 years, find the mean. Since… z= x-μ σ Then… x = μ + zσ 6. 9944 = μ + z 1. 53 0. 07 6. 9944 = μ + (1. 48)1. 53 μ = 4. 73 0. 43 The TV tube lasts an average of 4. 73 years. z 0. 00 0. 01 0. 02 0. 03 0. 04 0. 05 0. 06 0. 07 0. 08 0. 09 - - - 1. 4 0. 4192 0. 4207 0. 4222 0. 4236 0. 4251 0. 4265 0. 4279 0. 4292 0. 4306 0. 4319

Steps 1) Write out what is given μ = 5 or σ = 1. 33 2) Draw a bell curve and fill in as much as possible z= x-μ σ 3) Write both formulas and pick which one you x = μ + zσ need 4) Plug in all values you know into the formula 5) Use the table in A 8 6) Subtract from. 5000? Add together?

From the HW P. 376 1) The shelf life of a dairy product is normally distributed with a mean of 11 days and a standard deviation of 2. 9 days. If a product is randomly selected, find the probability that it will last between 10 and 15 days. 54. 93%

HW P. 377 #1 -11 or #1 -11 Odds if you bring in at least 3 canned food drive items Note: HW will be cleared out at the end of the week