Pasadena City College Math 50 Midterm 2, Chapter 4-6; Triola- Elementary Statistics.
1.Clinical Test of Lipitor. The cholesterol-reducing drug Lipitor consists of atorvastatin calcium.
If one of the 100 subjects is randomly selected, find the probability of:
Treatment__________________
10-mg Atorvastatin
Placebo_____Total
Headache
15
65
80
No headache
17
3
20
Total
32
68
100
a) getting someone who had a headache and was treated with a placebo.
b) getting someone who had a headache or was treated with 10 mg of atorvastatin.
c) that he or she had no headache, given that the subject was treated with 10 mg of atorvastatin.
d) If two subjects are randomly selected, find the probability of getting two people who were
treated with a placebo (w/o replacement)
2) Assume a standard deck of cards. Find the probability of getting a heart, given that the card
selected is a king.
3) There are 3 red, 2 orange and 4 yellow m&m’s in a bag. If you randomly select three m&m’s,
find the probability of getting 2 red and 1 yellow m&m in any order (write answer as a decimal).
4) There are three multiple choice questions (with 4 choices each). If you guess on all three
questions, what is the probability of getting at least one correct answer?
5) If a die is rolled three times, find the probability of rolling a 4 each time?
6) What is the probability of winning the lottery if you must choose five numbers from 1
through 49. (note: numbers cannot repeat and the order in which the numbers were drawn is not
important).
7) How many ways can a chair and assistant chair be selected from a group of 3 people?
8) A code must consist of two digits followed by two letters (w/ replacement) if digits may
repeat but the first digit cannot be a zero, how many different codes are possible?
9) Find the probability that when a couple has 3 children, they have exactly 2 boys.
(hint: writing the sample space may be helpful)
10) a roulette wheel is spun. 38 slots (18 red, 18 black, and 2 green).
a) What is the probability of getting red or green?
b) What is probability of getting a green?
11. The organizer of a television show must select 5 people to participate in the show. The
participants will be selected from a list of 25 people who have written in to the show. How many
different 5-person participants are possible?
12. In a study of chocolate preference among chocolate lovers, 432 chocolate lovers said they
prefer See’s Candy and 324 said they prefer Godiva. Estimate the probability that a randomly
selected chocolate lover will prefer See’s Candy?
13. Let the random variable x represent the number of girls in a family of ten children. (a) Write
down the Binomial-Distribution formula for this Probability distribution p(x). (b) Find the mean
and standard deviation of x (you need not use part (a))
14. A Fidelity life insurance company charges $226 for a $50,000 life insurance policy for a 50
year-old-female. The probability that such a female survives the year is 0.9968. Assume that the
company sells 700 such policies to 50-year-old females, so it collects $158,200 in policy
payments. The company will make a profit if fewer than 4 of the 700 females die during the year.
(a) What is the mean number of deaths in such a group of 700 females? b) Find the probability
that the company makes a profit?
15. Neuroblastoma, a rare form of malignant tumor. 4 cases occur in Oak Park Illinois which had
12,429 children. Assuming a Poisson distribution is relevant here, find:
(a) The mean number of cases in a group of 12,429 children. (b) Find the probability that the
number of Neuroblastoma among 12,429 children is 0 or 1. (c) What is the probability of more
than one case?
16. Find the standard z-score with (a) Cumulative area to the left of 0.6700. (b) Cumulative area
to the right of 0.9960 (c) Z 0.025
17. Assess the normality of the data set below by creating an appropriate table and plotting the
points:
{2, 3,  1, 1} and   1 while   2.
18. Assume the heights of men are normally distributed with mean 69.0in and standard deviation
of 2.8in. In designing a new bed you want you want the length of the bed to equal or exceed the
height of 95% of all men. What is the min bed length required?
19. A large number of SRSs of size n=85 are obtained from a large population of birth weights
having a mean of 3420g and a standard deviation of 495g. The sample mean is computed for
each sample.
(a) What is the approximate shape of the distribution of the sample-means?
(b) What is the expected mean of the sample-means?
(c) What is the standard deviation of the sample-means?
20) As reported by the US National Center for Health Statistics, the mean cholesterol of females
20 to 29 years old is µ= 53. If cholesterol is normally distributed with s.d = 13.4, answer the
following:
a) What is the probability a randomly selected female 20 to 29 yrs old has a cholesterol
above60.
b) What is the probability a random sample of 15 female 20 to 29 years old has a mean
cholesterol above 60?
c) The probability that a random sample of 20 females 20 to 29-years-old has a mean
cholesterol above 60 is less than the probability in part b. Use the CLT to explain why the
increased sample size results in this lower probability.
d) What might you conclude if a random sample of 20 female 20 to 29 year-olds has mean
serum cholesterol above 60?