A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The outcomes are listed in the table below. Note that each outcome has the same probability.
For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event.
/
What are the outcomes for each and the probability
More tails than heads {HTT,THT,TTH,TTT} 1/2
Exactly one tail {THH,HTH,HHT} 3/8
A head on the last toss {HHH,HTH,THH,TTH} 1/2
2. A purchasing manager at a university is investigating which brand of LCD projector to purchase to equip "smart" classrooms. Of major concern to her is the lifetime of the light bulbs used in the projectors. One company has published the following information regarding the lifetimes of a sample of bulbs used in its
Based on the histogram, find the proportion of bulb lifetimes in the sample that are greater than or equal to hours. Write your answer as a decimal, and do not round your answer.Answer: 0.06
3. Bids were placed in a silent auction for a sword reputed to have been used at the Battle of Hastings, worth a reported . The respective bids (in thousands of dollars) placed by the bidders were as follows:
18, 20, 18, 29, 18, 24, 20, 20
A)What is the mean of this data set? If your answer is not an integer, round your answer to at least one decimal place.
Answer: 20.9
B)What is the median of this data set? If your answer is not an integer, round your answer to at least one decimal place.
Answer: 20
C) How many modes does the data set have, and what are their values? Indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s) if applicable
Answer, the data set have 2 modes and the values are 18 and 20
- Below are the times (in days) it takes for a sample of customers from Jack's computer store to pay their invoices.
26, 42, 18, 31, 22, 17
Find the standard deviation of this sample of times. Round your answer to at least two decimal places.
Answer: 9.40
Students at a major university are complaining of a serious housing crunch. Many of the university's students, they complain, have to commute too far to school because there is not enough housing near campus. The university officials respond with the following information: the mean distance commuted to school by students is miles, and the standard deviation of the distance commuted is miles.
Assuming that the university officials' information is correct, complete the following statements about the distribution of commute distances for students at this university.
A)According to Chebyshev’s theorem, at least 75% of the commute distances lie between 9.9 miles and 23.9 miles
B)According to Chebyshev’s theorem, at least 55.6% of the commute distances lie between 11.65 miles and 22.15 miles.
C)Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 95% of the commute distances lie between 9.9 miles and 23.9 miles
D)Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the commute distances lie between 6.4 miles and 27.4 miles.
- An ordinary (fair) die is a cube with the numbers through on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events:
Event : The sum is greater than .
Event : The sum is not divisible by and not divisible by .
Write your answers as exact fractions.
Answers: P(A)=5/18, P(B)=5/9
8. A sample of adults is selected. The adults are classified according to their voter registration status and their preferred source of current events information. The results are given in the contingency table below.
Preferred source of informationTelevision / Newspapers / Radio / Internet sites
Voting registration status / Registered / 15 / 19 / 15 / 47
Not registered / 18 / 29 / 18 / 39
Among the adults in the sample who prefer to obtain their information through television, what is the relative frequency of those who are not registered to vote?
Round your answer to at least two decimals places.
Answer: 0.55
Questions 1-3 refer to the records of two basketball teams. We define "free throw success rate" as the fraction of free throw attempts that succeed in scoring a point. For each team, we obtain each player's free throw success rate. Assume that the distribution of this variable is normal for both teams. The average free throw success rate for the two teams is identical, 0.81. The standard deviation is 0.05 for Team A and 0.10 for Team B.Which team probably has the player with the highest free throw success rate?
Team A
Team B
Answer: B
Which team probably has the player with the lowest free throw success rate?
Team A
Team B
Answer: B
Which team's players have a more consistent free throw success rate?
Team A
Team B
Answer: A
Now let's review something that's truly magical, the Central Limit Theorem (CLT).
The Central Limit Theorem says…
There are limits to everything.
Everything tends to a medium value.
The sampling distribution of the sample mean is normal.
A variable's mean is limited to the central part of its distribution.
Answer: The sampling……..
The CLT says the mean of the sampling distribution of the mean is…
The population mean multiplied by the sample size.
The population mean.
The population mean divided by the sample size.
The population mean divided by the square root of the sample size.
Answer: the population mean
The CLT says the standard deviation of the sampling distribution of the mean is…
The population standard deviation multipled by the sample size.
The population standard deviation.
The population standard deviation divided by the sample size.
The population standard deviation divided by the square root of the sample size.
Answer: The population standard deviation divided by the square root of the sample size.
Now some questions about general statistical topics.
The standard normal distribution has a mean of…
0
1
π = 3.14159
Depends on degrees of freedom
Answer: 0
The standard normal distribution has a standard deviation of…
0
1
π = 3.14159
Depends on degrees of freedom
Answer: 1
When you choose between using the normal distribution and Student's t distribution, and when the population standard deviation is unknown, you must choose t when…
Sample variance is known.
Population variance is known.
Sample variance is unknown.
Population variance is unknown.
Answer: I am not sure about this one since the answer is in the text
Put the last option: Population variance is unknown
The continuous probability distribution depicted in the graph at right is…
Symmetric
Positively skewed
Negatively skewed
Not skewed
Answer: Negatively skewed
The population standard deviation is usually denoted by…
s
μ
σ
Answer:
The sample standard deviation is usually denoted by…
s
μ
σ
Answer: s
A measurable characteristic of a population is called a …
Census
Frequency distribution
Statistic
Parameter
Answer: parameter
A measurable characteristic of a sample is called a…
Census
Frequency distribution
Statistic
Parameter
Answer: Statistic
In statistical hypothesis testing, which of these can sometimes be proved?
Null hypothesis
Alternative hypothesis.
Both
Neither
Answer: Neither
In statistical hypothesis testing, which of these can sometimes be rejected?
Null hypothesis
Alternative hypothesis.
Both
Neither
Answer: Null hypothesis
The graphic at right depicts a normally distributed random variable,X. the distribution has a mean of 100 and a standard deviation of 10. Choose the best answer for each question.
What is the probability that X is greater than 100?
0.00
0.025
0.50
0.68
0.95
Answer: 0.5
What is the probability that X lies between 90 and 110?
0.00
0.025
0.50
0.68
0.95
Answer: 0.68
What is the probability that X is less than 80?
0.00
0.025
0.50
0.68
0.95
Answer: 0.025
What is the probability that X is exactly equal to 100?
0.00
0.025
0.50
0.68
0.95
Answer: 0.00
Graph 1 is for question number 10…and graph 2 is for question numbers 17-20