Download Quiz #1 - Cabrillo College

Math 12
Quiz #1
Fall 2014
Name:
Directions:
Select the term that best describes the following statements.
1) A subset of the employees from a large company is randomly selected, and the average age
among this sample is calculated to be 37 years old. What is this quantity?
A. Statistic
B. Parameter
2) The number of freshman entering college in a particular year is 621. Given this background
what type of number is 621?
A. Continuous
B. Discrete
3) What kind of a variable results from a survey asking respondents to categorize performance as
"good, better, or best"?
A. Nominal
B. Interval
C. Ratio
D. Ordinal
4) A town obtains the current employment data by polling 10,000 of its citizens randomly. What
kind of study is this?
A. Retrospective
B. Cross-sectional
C. Longitudinal
D. Controlled Experiment
5) The student body is divided into categories of Freshman, Sophomores, Juniors, and Seniors
with 621, 496, 348, 481 student respectively. 60, 49, 34, and 48 students are randomly sampled
from each of the categories respectively; what type of sampling is this?
A. Convenience
B. Cluster
C. Random
D. Systematic
E. Stratified
Math 12
Quiz #2
Fall 2014
Name:
Jonny Tsunami recently started taking classes at Cabrillo College, but he still
wants to make time every day to go surfing. Jonny’s class schedule only affords
him an hour of surfing time between 1pm and 2pm every day. However Jonny
does not normally surf at this time of the day, and he is not sure how good
the waves will be. In order to characterize his expectations Jonny decides to
start collecting data. Every day from 1pm to 2pm Jonny watches the waves;
at the end of his hour long window, each day, he records the total number of
“gnarly” waves that he has observed. After collecting data of this type for 16
days Jonny feels confident that he has enough data to begin his analysis. The
chart to the right contains the raw data that Jonny collected in each of his 16
days of wave observation. Use these data to answer the following questions.
Number of
“gnarly” waves
1) What is the mean number of “gnarly" waves?
2) What is the median number of “gnarly" waves?
3) What is the mode of the observed number of “gnarly" waves?
4) Which measure of center do you think is most appropriate for this data, and why?
5) What is the variance in the observed number of “gnarly" waves?
6) Is this data skewed? If so, what kind of skew?
1
2
0
0
0
1
0
5
2
1
0
1
4
1
3
1
Math 12
Quiz #3
Fall 2014
Name:
Recall Jonny Tsunami and his search for “gnarly” waves. Jonny’s study of “gnarly” waves found
the distribution of the number of “gnarly” waves had a mean of 1.375 “gnarly” waves and a standard
deviation of 1.5 “gnarly” waves. You may also recall that this distribution had a right skew. This
week we will ignore the skew in Jonny’s data and assume that Jonny’s population of interest has a
distribution that is well modeled by a normal distribution with Jonny’s mean and standard deviation.
That is, assume that the population distribution for the number of “gnarly” waves is N (1.375, 1.5)
(i.e. a normal distribution with µ = 1.375 and σ = 1.5).
Given this population distribution let’s determine if these waves will satisfy Jonny’s surfing needs.
Jonny states that a given surfing session is a “radical” surfing session if he observes at least 3 “gnarly”
waves in that surfing session. Use this information to answer the following questions.
1) What is the probability that Jonny’s next surf outing will be a “radical” surfing session?
hint: Find the probability that the # “gnarly” waves observed will be at least 3.
2) What is the probability that Jonny’s next surf outing will not be a “radical” surfing session?
3) Do you think that Jonny is likely to be satisfied with his next surf outing?
4) What is the probability that Jonny experiences at least 1 “radical” surfing session in a total of
2 surf outings?
Math 12
Quiz #4
Fall 2014
Name:
Once again recall our boy, Jonny Tsunami, the surfer. On a good day Jonny is capable of catching
6 waves in a single surfing session. However, this only occurs if Jonny is able to successfully catch
every wave that he attempts to catch. That is to say, in every surfing session Jonny always attempts
to catch exactly 6 waves, but only on the best of days does Jonny successfully catch all 6 of these
waves. Assume that the probability that Jonny will successfully catch any particular wave is 0.75.
Use the above provided information to answer the following questions.
1) What is the probability that Jonny will surf a perfect session, thus successfully catching all 6
of the 6 waves that he attempts to catch in a given session?
hint: Use the binomial distribution.
2) What is the probability that Jonny will not surf a perfect session?
hint: Do not use the binomial distribution directly.
3) Recall that Jonny is not just looking for any wave, but in particular he is looking for “gnarly”
waves. Assume that “gnarly” waves occurs with a probability of 0.2. What is the probability
that exactly 3 of the 6 waves that Jonny attempts to catch will be “gnarly” waves?
4) If we assume independence between Jonny’s wave catching ability and the type of wave that he
is attempting to catch, what is the probability that {Jonny has a perfect session} and {exactly
3 of those 6 waves are “gnarly” waves}?
Math 12
Quiz #5
Fall 2014
Name:
1) One day as Jonny Tsunami is heading down into the water to go surfing, he runs into a wise old
fisherman. The fisherman tells Jonny that, on average, over an hour long observation period
fish
). When Jonny gets into the water
Jonny should expect to see an average of 4 fish (i.e. 4 hour
he decides to count each fish that he sees over his hour long surfing session that day. What is
the probability that he observes exactly 4 fish during his surfing session?
2) It seems that Jonny has picked up a nasty gambling habit. After his surf session each day
Jonny goes to play dice with the sailors at the port adjacent to his favorite surfing spot. If we
assume Jonny and the sailors play with fair dice (i.e. the probability of rolling any particular
number is always 16 on a given roll), what is the probability that Jonny will roll exactly 2 ’s
in a total of 6 dice rolls?
3) Assume that Jonny’s daily winnings (in USD) from rolling dice follow a normal distribution,
such that in the long run his average winnings are 0 USD and the variance is 1 USD2 . What
is the probability that Jonny will not lose money on a given day?
4) Recall that the normal distribution is continuous. If we assume the same distribution for
Jonny’s daily winnings described in question 3), what is the probability that Jonny will win
exactly 1 USD on a given day?
Math 12
Quiz #6
Fall 2014
Name:
Recall that at the beginning of the semester Jonny Tsunami did a small study of the number of
“gnarly” waves at his favorite surf spot. Jonny’s study resulted in a single sample of size n = 16, with
each data point representing the number of “gnarly” waves observed on each of his 16 observation
days. Jonny’s sample of the number of “gnarly” waves had the following sample summary statistics:
x̄ = 1.4
Median = 1.0
Mode = 1.0
s2 = 2.3
1) If we wanted to consider the repeated sampling distribution of the means, would the Central
Limit Theorem (CLT) apply? If so, why? If not, why not?
2) Regardless of your answer to 1) assume, for the rest of the quiz, that we can get away with
using the CLT. If I give you the population parameters for the distribution of “gnarly” waves,
µ = 2 and σ 2 = 1.25, what is the distribution of the average number of waves? Draw me a
picture.
3) Using the information from 2) above, what is the z-score of the sample mean that Jonny saw
relative to the repeated sampling distribution of means?
4) What is the probability of seeing a mean that is as extreme or more extreme (i.e. in either
direction) than the mean that Jonny saw?