Here is a list of the problems. Answers need to be provided in the attached Word document.
1.The
singular form of the word “dice” is “die”. Tom was throwing a six-sided die.
The first time he threw, he got a three; the second time he threw, he got a
three again. What’s the probability of getting a three at the third time? 2.There are 30 table tennis balls in the box: 6
are green, 10 are red, and 14 are yellow. If you shake the box and then
randomly select one ball from the box, what’s the probability that you will get
a red one: 3. Rachel was flipping a coin with Jerry. She
told jerry: “I am able to get all heads in two tosses.” Jerry laughed at her:
“No, the probability of getting two heads at two tosses is only__” 4. Jennie and Alex both wanted to get a free
ticket for a College Music concert. However, the concert staff told them the
tickets were limited. Twenty people wanted to attend the concert but only 10
free tickets were left. So the concert center staff decided to use a lottery to
decide who would receive the free tickets. What’s the probability of Jennie and
Alex both getting free tickets? 5.Laura and Melissa were playing dice. What the probability of Laura and
Melissa both getting a 6? 6. In a statistics class with 36 students, the
professor wanted to know the probability that at least two students share the
same birthday. The probability will be___ a. 0.1 b. Much
smaller than 0.1 c. Much
bigger than 0.1 d. Not
possible 7. If you throw a die for two times, what is the
probability that you will get a one on the first throw or a one on the second
throw (or both)? 8. Jerry got a box full of colorful candy balls.
There were 50 of them: 20 red, 10 green, 12 yellow and 8 blue. After shaking
the box, he randomly selected 2 candy balls from the box. What’s the
probability that the first one was blue and the second one was yellow? 9.Jerry got a box full of colorful candy balls. There were 50 of them: 20
red, 10 green, 12 yellow and 8 blue. After shaking the box, he randomly
selected 2 candy balls from the box. What’s the probability that the first is
blue and the second one is also blue? 10. Which activity could probabilities be computed using a Binomial
Distribution? a. Flipping a
coin a 100 times b. Throwing a
die one hundred times c. The
probability of getting a heart while playing card games d. Grades
earned by 100 students on a statistics final exam 11. Many researchers have argued that
the TB skin test is not accurate. Imagine that the TB skin test is only 70%
accurate. Sarah is thinking about having the test. Before she has the test she
wonders the probability that she has TB. The probability of Sarah having TB is
… a. 70% b. 35% c. 30% d. More information needed to calculate 12. Imagine that the diabetic test
accurately indicates the disease in 95% of the people who have it. What’s the
miss rate? 13. Which of the following is the probability that subjects do not have
the disease, but the test result is positive? a. Miss rate b. False
positive rate c. Base rate d. Disease
rate 14. In a normal distribution, the median is ____it’s mean and
mode. a. Approximately
equal to b. Bigger
than c. Smaller
than d. Unrelated
to 15. In a normal distribution, __ percentage of the area under
the curve is within one standard deviations of the mean? a. 68% b. 100% c. 95% d. It
depends on the values of the mean and standard deviation 16. A normal distribution with a mean of 15 and standard
deviation of 5. 95% of its area is within__ a. One
standard deviation of the mean b. Two
standard deviations of the mean c. Three
standard deviations of the mean d. It
depends on the value of the mode 17.The mean of a standard normal
distribution is: a. 0 b. 1.0 c. -1.0 d. 100 18. The standard deviation of the mean for a standard
distribution is: a. 0.0 b. 1.0 c. 100 d. 68% 19. A normal distribution with a mean
of 25 and standard deviation of 5. What is the corresponding Z score for a case
having a value of 10? 20. Consider
a normal distribution with a mean of 25 and standard deviation of 4.
Approximately, what proportion of the area lies between values of 17 and 33. a. 95% b. 68% c. 99% d. 50% 21. Consider a normal distribution
with a mean of 10 and standard deviation of 25. What’s the Z score for the
value of 35? 22. For a standard normal distribution, what’s the probability
of getting a positive number? a. 50% b. 95% c. 68% d. We
cannot tell from the given information 23.Two-hundred students took a
statistics class. Their professor creatively decided to give each of them their
Z-score instead of their grade. Rachel got her Z-score of -0.2. She was
wondering how well she did on the exam. a. It
was very good, much better than almost all of the other students b. It
was so-so, but still better than half of the students. c. It
was not that good, but not at the bottom of the distribution d. It
was very bad and she needs to work much harder next time 24. A researcher collected some data and they form a normal
distribution with a mean of zero. What’s the probability of getting a positive
number from this distribution? a. 25% b. 50% c. 75% d. We
need to calculate the standard deviation and then decide. 25. Which of the following description of distribution is
correct? a. A
Binomial distribution is a probability distribution for independent events for
which there are only two possible outcomes b. You
cannot use the normal distribution to approximate the binomial distribution c. Normal
distributions cannot differ in their means and in their standard deviations. d. Standard
normal distributions can differ in their means and in their standard
deviations. 26. A toy factory makes 5,000 teddy
bears per day. The supervisor randomly selects 10 teddy bears from all 5,000
teddy bears and uses this sample to estimate the mean weight of teddy bears and
the sample standard deviation. How many degrees of freedom are there in the
estimate of the standard deviation? 27. Imagine you have a population of 100,000 cases. For which of
the following degrees of freedom is the closest estimation of the population
parameter? a. 4 b. 6 c. 10 d. 1000 28.Imagine that the average weight of a
total of 500 girls in a high school is 35kg. Tom randomly sampled 10 girls and
measured their weight. And then he repeated this procedure for three times. The
means and standard deviations are listed as following. Which sample estimate
shows the least sample variability? a. Sample
one: mean=34, SE=5 b. Sample
two: mean=30, SE=2 c. Sample
three: mean= 26, SE=3 d. Sample
four: mean= 38, SE=5 29. For which of the following degrees of freedom is a t
distribution closest to a normal distribution? a. 10 b. 20 c. 5 d. 1000 30. In order to construct a confidence interval for the
difference between two means, we are going to assume which of the followings?
(Select all that apply) a. The
two populations have the same variance. b. The
populations are normally distributed. c. Each
value is sampled independently from each other value. d. The
two populations have similar means 31. A researcher tries to compare
grades earned on the first quiz by boys and girls. He randomly chooses 10
students from boys and 15 students from girls and calculates the confidence
interval on difference between means. How many degrees of freedom will you get
in this t distribution? 32. Which of the following choices is not the possible
confidence interval on the population values of a Pearson’s correlation? a. (0.3,
0.5) b. (-0.7,
0.9) c. (-1.2,
0.3) d. (0.6,
0.8)33. Which of the following descriptions
of the t distribution is correct? (Select all that apply) a. With
smaller sample sizes, the t distribution is leptokurtic b. When
the sample size is large (more than 100), the t distribution is very similar to
the standard normal distribution c. With
larger sample sizes, the t distribution is leptokurtic d. The
t distribution will never be close to normal distribution 34. _________________refers to whether or not an estimator tends
to overestimate or underestimate a parameter. ______________ is the standard
deviation of the sampling distribution and play a critical role in the
constructing confidence intervals and in significance testing.a. Bias;
standard error b. Sample
population; Bias c. Mean;
standard deviation d. Standard
deviation; Mean 35. Which of the following descriptions of confidence intervals
is correct? a. Confidence
intervals can only be computed for the mean b. We
can only use the normal distribution to compute confidence intervals c. Confidence
intervals can be computed for various parameters d. Confidence
intervals can only be computed for the population
