Download Section 5.1 models of random behavior

Section 5.1 Constructing Models of Random Behavior
Statistics
(Questions from pages 297 – 301 of text)
P2.) The table below gives the actual low temperature (to the nearest 50F) in
Oklahoma City on days when the National Weather Service forecast was
for a low temperature of 300F.
Actual Low
Frequency
Temperature (0F)
20
2
25
8
30
13
35
3
40
1
a.) Suppose the forecast for tomorrow is for a low temperature of 300F.
What is your estimate of the probability that the low temperature
really will be approximately 300F?
b.) Using these data, make a table that gives the estimated probability
distribution for the actual low temperature when the forecast is 30 0F.
c.) Does the method of forecasting appear to give a prediction that tends,
on average, to be two warm, or too cold?
P3.) Suppose you flip a coin and then roll a die. If you get heads and a 3, then
your outcome is H3.
a.) List a sample space that has outcomes that are disjoint and complete.
b.) Are all outcomes in your sample space equally likely?
c.) What is the probability that you get heads and a 3?
P4.) You randomly choose two workers to be laid off from a group of workers
ages 28, 35, 41, 47, and 55.
a.) List a sample space that has outcomes that are disjoint and complete.
b.) Are all outcomes in your sample space equally likely?
c.) What is the probability that the two youngest people are the ones laid
off?
d.) What is the probability that the mean age of those laid off is 40 or
more?
P6.) Suppose you pick four students at random from your school and check
whether they are left-handed or right-handed.
a.) Can you list a sample space?
b.) Can you determine the probability that all four students are righthanded?
P7.) The results of 50 spins of a penny are plotted in Display 5.8 on page 298
(you need to look at this to answer most of this question). The horizontal
axis gives the number of the spin, and the vertical axis gives the
cumulative proportion of spins so far that were heads.
a.) Was the first spin heads or tails?
The Second?
The Third?
The Fourth?
b.) Use these data to estimate the probability that this penny will land
heads up when it is spun.
P8.) Suppose you ask a person to taste a particular brand of strawberry ice
cream and evaluate it as good, okay, or poor on flavor and as acceptable or
poor on flavor and as acceptable or unacceptable on price.
a.) Show all possible outcomes on a tree diagram.
b.) How many possible outcomes are there?
c.) Are all the outcomes equally likely?
P9.) A dental clinic has three dentists and seven dental hygienists.
a.) If you are assigned a dentist and a dental hygienist at random when
you go in, how many different pairs could you end up with?
b.) What is the probability that you get your favorite dentist and your
favorite dental hygienist?
c.) Illustrate your answer in part a.) with a two-way table.
d.) Illustrate your answer in part a with a tree diagram.