Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Honors Statistics
Aug 23-8:26 PM
1. Collect folders and materials
2. Continue Binomial Probability
3. Review OTL C6#11 homework
4. Binomial mean and standard deviation
5. Past Homework discussion
6. Return materials
Jan 18-5:03 PM
1
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
May 13-11:55 AM
Continue Final Exam Review LSRL pg 1 & 2
Jan 30-12:31 PM
2
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Random digit dialing When an opinion poll calls a residential telephone number at
random, there is only a 20% chance that the call reaches a live person. You watch the
random digit dialing machine make 15 calls. Let X = the number of calls that reach a live
person.
B(15, 0.2)
(a) Find and interpret µx.
µx = np = 15(0.20) = 3 calls that reach a live person
If we observe the random digit dialing machine make
many sets of 15 random calls, we would expect to
average 3 calls that reach a live person.
(b) Find and interpret σX.
σx =
√ 15(0.20)(0.80) = 1.55 calls that reach a live person
If we observe the random dialing digit machine make on
set of 15 random calls, the number of live persons the
machine reaches will typically differ from the average of
3 calls reaching a live person by about 1.55 calls.
Jan 27-7:10 PM
Random digit dialing
Refer to Exercise 81. Let Y = the number of calls that don’t reach a live person.
(a) Find the mean of Y. How is it related to the mean of X? Explain why this makes sense.
Now B(15, 0.8)
µy = np = 15(0.80) = 12 calls that reach a live person
This makes sense in a binomial setting because there are only
two outcomes and 3 + 12 = 15 calls
(b) Find the standard deviation of Y. How is it related to the
standard deviation of X? Explain why this makes sense.
σy =
σx =
√ 15(0.80)(0.20) = 1.55 calls that reach a live person
√ 15(0.20)(0.80) = √ 15(0.80)(0.20) =
σx = σy
σy
due to the commutative property, the standard deviation is
being calculated for the same binomial situation (that would have the
same variability) and Y = 15 - X (measures of spread are not affected
by adding a constant to each individual variable
Jan 27-7:10 PM
3
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Aircraft engines Engineers define reliability as the probability that an item will
perform its function under specific conditions for a specific period of time. A
certain model of aircraft engine is designed so that each engine has probability
0.999 of performing properly for an hour of flight. Company engineers test an
SRS of 350 engines of this model. Let X = the number that operate for an hour
without failure.
(a) Explain why X is a binomial random variable.
Binomial setting: Operate for one hour OR does not operate for one hour
n is fixed n = 350 engines
p = 0.999 success rate of design is the same for all engines
Independence? This is implied by the selection of the SRS
(b) Find the mean and standard deviation of X. Interpret each value in context.
µx = np = 350(0.999) = 349.65
If we were to test many, many sets of 350
randomly selected engines we would expect
349.65 to operate properly for 1 hour.
σx =
√ 350(0.999)(0.001) = 0.591
If we were to test a set of 350 randomly selected engines, the
number of engines that operate properly for one hour would typically
deviate from 349.65 by 0.591 engines.
(c) Two engines failed the test. Are you convinced that this model of engine is
less reliable than it’s supposed to be? Compute P(X ≤ 348) and use the result to
justify your answer.
Use binomialcdf(350, 0.999,348) =
The probability that 2 or more engines would fail is expected to be 0.0489 or 4.86% chance.
This does seem rather high for the (0.999) claim. However I am not sure we are testing the
correct question.
binomialpdf (350,0.999, 2) ≈ 0.0
Jan 27-7:10 PM
101.
Joe reads that 1 out of 4 eggs contains salmonella
bacteria. So he never uses more than 3 eggs in cooking.
If eggs do or don’t contain salmonella independently of
each other, the number of contaminated eggs when Joe
uses 3 chosen at random has the following distribution:
B
>
(a) binomial; n = 4 and p = 1/4
>
(b) binomial; n = 3 and p = 1/4
>
(c) binomial; n = 3 and p = 1/3
>
(d) geometric; p = 1/4
>
(e) geometric; p = 1/3
May 13-10:26 AM
4
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Exercises 102 and 103 refer to the following setting. A fast-food restaurant runs a
promotion in which certain food items come with game pieces. According to the
restaurant,1 in 4 game pieces is a winner.
102. If Jeff gets 4 game pieces, what is the probability that he wins exactly 1 prize?
C > (a) 0.25
>
(b) 1.00
>
(c)
>
(d)
>
(e) (0.75)3(0.25)1
May 13-10:39 AM
Exercises 102 and 103 refer to the following setting. A fast-food restaurant runs a
promotion in which certain food items come with game pieces. According to the
restaurant,1 in 4 game pieces is a winner.
103.
If Jeff keeps playing until he wins a prize, what is the probability that he has to
play the game exactly 5 times?
D
> (a) (0.25)5
> (b) (0.75)4
> (c) (0.75)5
> (d) (0.75)4(0.25)
> (e)
May 13-10:42 AM
5
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Each entry in a table of random digits like Table D has probability 0.1 of
being a 0, and the digits are independent of one another. If many lines of 40
random digits are selected, the mean and standard deviation of the number
of 0s will be approximately
D
> (a) mean = 0.1, standard deviation = 0.05.
> (b) mean = 0.1, standard deviation = 0.1.
> (c) mean = 4, standard deviation = 0.05.
> (d) mean = 4, standard deviation = 1.90.
> (e) mean = 4, standard deviation = 3.60.
May 13-10:42 AM
0.2373 0.3955
0.2373
0.2637
0.0879
0.0146
0.000977
0.63281 0.89648 0.98437 0.99902 1.00000
Jan 30-5:53 PM
6
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Jan 30-5:53 PM
Feb 2-1:34 PM
7
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Feb 2-1:34 PM
Jan 27-2:30 PM
8
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Jan 28-8:10 PM
Jan 27-2:34 PM
9
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
is the ability to recognize situations to which they do
BE Careful. These short formulas are good only for
Dec 12-12:40 PM
Jan 28-8:10 PM
10
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Jan 28-8:12 PM
Jan 30-6:09 PM
11
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Dec 11-7:31 PM
Dec 11-7:58 PM
12
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
situation.
Dec 12-12:51 PM
until you observe a jack.
Dec 12-12:54 PM
13
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Dec 12-12:57 PM
Feb 3-10:30 AM
14
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Dec 11-7:57 PM
Dec 12-1:04 PM
15
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Dec 12-12:44 PM
How many times should we expect to roll a die until
Dec 12-1:15 PM
16
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Dec 12-1:14 PM
disk drives are defective. You have been asked to determine the
Jan 28-2:49 PM
17
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
Jan 28-2:53 PM
Jan 28-12:42 PM
18
Chapter 6 Section 3 day 3 Geo 2016 Notes.notebook
May 17, 2016
OTL C6#13
Jan 30-12:31 PM
19