(HW_4_1) A landscape designer is designing a large garden for a
new home. The client is particularly fond of palms and would like to have
them included. The landscape designer knows that in the local climate,
palms are given only a 30% chance of surviving the first year. Generally,
if the palms survive the first year, they will continue to flourish. The
landscape designer is considering a design which includes a random sample
of 11 palms (not from the same root stock). Let X be the number of palms
that survive the first year after planting.
Discuss the validity of using the Binomial distribution in this situation.
(Hint: consider the conditions for this distribution and consider how well
these conditions are satisfied here).
State the value of the parameter(s) of this distribution.
Assuming that the distribution you have described above is an appropriate
model for X, find the probability that:
no more than 3 of the palms survive the first year.
only 1 of the palms survive the first year.
between 2 and 6 palms (inclusive) survive the first year.
How many palms would you expect to survive the first year? What is the
standard deviation of X?
(HW_4_2) A medical trial was conducted to investigate whether a
new drug extended the life of patients who had lung cancer. The survival
times (in months) for 38 cancer patients who were treated with the drug
are as follows:
1
1
5
9
10
13
14
17
18
18
19
21
22
25
25
25
26
27
29
36
38
39
39
40
41
41
43
44
44
45
46
46
49
50
50
54
54
59
Sample mean ~= 31.1 months and standard deviation ~=
16.0 months.
Assume that the survival time (in months) for patients on this drug is
Normally distributed with a mean of 31.1 months and a standard deviation
of 16.0 months.
What is the probability that a patient survives for no more than one year?
What proportion of patients will survive between one year and two years?
What is the highest survival time that 80% of patient survival times exceed?
Calculate the central 80% of survival times.
Draw a stem-and-leaf plot of the number of months of survival for these
38 patients.
Does the plot give us any reason to question the assumption that the survival
times are Normally distributed?
\Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology,
UCLA School of Medicine/