Supplementary Final Test
Preparation. Material after Midterm I and II
Remember that the final test is
cumulative.
TI 83 format of probability
distribution.
Normalpdf
e
Normalcdf(lower bound, upper
bound, mean, standard deviation)= 
Also notice that TI 83 uses
-
–1E99 , 
1E99
Poisson Distribution
. 
, with 
=
Poissonpdf
= 
Poissoncdf
=
Binomialpdf(n,p,x)=P(X=x)=
Binomialcdf(n,p,x)=
[1] The probability that a person loses weight from a certain diet program is 0.7. Among 40 people in the program,
(a) What is the probability that at least 30 people lose weight?
(b) What is the probability that between 16 and 18 people lose weight?
(c) Find the expected value, i.e., and the average number of people who will lose weight.
(d)
Find the standard deviation 
of this deviation.
[2]The probability to win a certain game is 0.6. What is the probability he wins his first game in the third try? I.e. he loses the first two games and wins the third.
[3]A certain area of Caribbean is, on the average, hit by 10 hurricanes a year. Find the probability that for a given year that area will be hit by
(a) Fewer than 8 hurricanes
(b) Anywhere between 10 to 12 hurricanes.
[4]A customer service center receives, on the average 6 phone calls an hour. Find the probability that for a given hour that there are
(a) 4 calls
(b) Between 6 to 8 calls
[5]Suppose that the location of a car accident in LIE West forms a uniform a uniform distribution between 2 km and 6 km from Exit 42. Find the probability the accident happens between 4 km and 6 km from Exit 42. Find the probability density function for this uniform distribution. Find the probability density function.
[6]The heights of 1000 students are normally distributed
with a mean of 175 cm and a standard deviation 
if 6.9 cm. How many of these students would you expect to
have heights
(c) less than 160 cm?
(d) between 171 and 182 cm?
(e) greater than or equal to 188 cm?
(f) Find the minimum height of a student to be in the upper 70%.
(g) Find the height k such that P(X < k) = 0.3
[7]A research scientist reports that mice will live an average of 40 months when their diets are enriched with vitamins. Assume that the life times of such mice are normally distributed with a standard deviation of 6.3 months; find the probability that a given mouse will live
(a) more than 32 months
(b) less than 28 months
(c) between 37 and 49 months?
(d) How many months do you expect when of 30% of those mice are still living.
[8]Find the value z if the area under Consider a normal
distribution with 
=40, 
=6.3 and its a normal curve.
(a) Find the area under the curve between z=37 and z=49
(b) Find the value z whose area under the normal curve to the left of z is 0.3
[9]Draw a standard normal curve. Indicate the maximum point and inflection point.
[10] (1) Describe the situation where one can use normal distribution as an approximation of binomial distribution.
Describe the situation where one can use Poisson distribution as an approximation of binomial distribution.
(2)Judy found that normal distribution and Poisson distribution are magic and she likes to use them as much as possible. She has two binomial situations. Decide which distribution she should use. Indicate the necessary parameter, erg mean, standard variation.
Situation A: 2000 people are tested. Probability of infection is 0.05.
Find F(X
100)
Situation B: 2000 people are tested. Probability of an individual gaining weight is 0.4.
Find F(X
750).