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
0.92360.5=0.4236 The area to the right of µ between 0 and 2.86 From the standard normal table, this area is
0.99790.5=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 taxfree 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 Taxfree municipal bonds ?(0.7257;0.7257)
Taxfree
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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 Spring '12
 vincent
 Normal Distribution

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