Stats_for_business4_chapt_5_

43 z 286 37 thecarmileagecase4 want the area under

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Unformatted text preview: standard normal 3. curve using the normal table (see the slide after that) curve 36 The Car Mileage Case #3 For x = 32 mpg, the corresponding z value is z= x − µ 32 − 33 − 1 = = = −1.43 σ 0.7 0.7 (so the mileage of 32 mpg is 1.43 standard deviations below (to the left of) the mean µ = 32 mpg) For x = 35 mpg, the corresponding z value is z= x − µ 35 − 33 2 = = = 2.86 σ 0.7 0.7 (so the mileage of 35 mpg is 2.86 standard deviations above (to the right of) the mean µ = 32 mpg) Then P(32 ≤ x ≤ 35 mpg) = P(-1.43 ≤ z ≤ 2.86) 37 The Car Mileage Case #4 Want: the area under the normal curve between Want: 32 and 35 mpg 32 Will find: the area under the standard normal Will curve between -1.43 and 2.86 curve 38 The Car Mileage Case #5 Break this into two pieces, around the mean µ The cumulative area to the left of µ between -1.43 and 0 By symmetry, this is the same as the area between 0 and 1.43 From the standard normal table, this area is 0.9236-0.5=0.4236 The area to the right of µ between 0 and 2.86 From the standard normal table, this area is 0.9979-0.5=0.4979 The total area of both pieces is 0.4236 + 0.4979 = 0.9215 Then, P(-1.43 ≤ z ≤ 2.86) = 0.9215 Returning to x, P(32 ≤ x ≤ 35 mpg) = 0.9215 39 Exercise: P254 • The yearly returns on common stocks are The approximately normally distributed with mean return of mean 12.4% and a standard deviation of 20.6%. standard • The yearly returns on tax-free municipal bonds are The approximately normally distributed with mean return of approximately 5.2% and a standard deviation of 8.6%. standard 40 Exercise: Continued Q: Find the probability that a random selected a) Common stock will give a positive yearly return. How about Tax-free municipal bonds ?(0.7257;0.7257) Tax-free c) Common stock will give a more than 10% return. (0.5478) d) Common stock will give a loss of at least than 10%. (0.1379) 41 Finding z Points on a Standard Normal Curve (e.g. find z.025) 42 Example 5.3 Stocking out of inventory Stocking out of inventory Example A large discount store sells blank VHS tapes want to large know how many blank VHS tapes to stock (at the beginning of the week) so that there is only a 5 percent chance of stocking out during the week chance • Let x be the random variable of weekly demand Let • Let st be the number of tapes so that there is only a 5% Let st probability that weekly demand will exceed st. st. • Want the value of st so that P(x > st) = 0.05 Want st st Given:x is normally distributed µ = 100 tapes σ = 10 tapes 10 43 Finding Z Poi...
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This note was uploaded on 09/16/2012 for the course 123 123 taught by Professor Vincent during the Spring '12 term at Ill. Chicago.

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