A recent survey asked UF students if they had a job or not, and if they were underclassmen (Freshmen and Sophomores) or uppercla
ssmen (Juniors and Seniors). The answers appear on the table below.
JOB NoJob
Underclassmen 40 37 77
Upperclassmen 42 39 81
82 76 158
Let A be the event that a student has a job, and let B be the event that a student is an underclassmen. Find P(AUB).
JOB NoJob
Underclassmen 40 37 77
Upperclassmen 42 39 81
82 76 158
Let A be the event that a student has a job, and let B be the event that a student is an underclassmen. Find P(AUB).
1 answer:
According to the table, a total of 158 students were surveyed (we can confirm this by either adding the total for upperclassmen or the total for those employed or not, which is displayed at the lower right corner of the table in the provided figure).
Remember that:
In the chart, each term is visually distinguished by a different color. To transform these figures into their corresponding probabilities, we must divide each by the overall student count. This is because the probability is determined by the count of favorable outcomes (in this case, a group fitting specified criteria) divided by the total count of outcomes (the overall number of participants surveyed). The answer can be found in the figure. For the intersection we are seeking, we need individuals who are both underclassmen and employed.
Remember that:
In the chart, each term is visually distinguished by a different color. To transform these figures into their corresponding probabilities, we must divide each by the overall student count. This is because the probability is determined by the count of favorable outcomes (in this case, a group fitting specified criteria) divided by the total count of outcomes (the overall number of participants surveyed). The answer can be found in the figure. For the intersection we are seeking, we need individuals who are both underclassmen and employed.
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Answer:
Based on the findings, we infer that the average cost of a wedding is lower than the $30,000 that was initially suggested.
Step-by-step explanation:
The following data set is provided: (in thousands)
29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600
Formula:
where denotes data points,
represents the mean, and n indicates the number of samples.
The sum of squares of the differences equals 3408750
The population mean, μ = $30,000
The sample mean, = $29512.5
Sample size, n = 8
Alpha, α = 0.05
Sample standard deviation, s = $697.82
Initially, we formulate the null hypothesis and the alternative hypothesis.
A one-tailed t-test will be conducted for this analysis.
Formula:
Thus, we conclude that the average wedding cost is indeed less than the advertised $30,000.
</pwe></pgiven></pnow></pinserting>1) 4.55
2) Short hit
Step-by-step explanation:
1)
The score and corresponding probabilities are shown in the following table:
Score 3 4 5 6 7
Probability 0.15 0.40 0.25 0.15 0.05
Let us define
X = Miguel's score on the Water Hole
The expected value of the variable X can be represented as:
where
represents the different possible outcomes of X
denotes the associated probabilities
Accordingly, the expected value of Miguel's score is calculated as follows:
2)
Here, we will again consider:
X = Miguel's score on the Water Hole
In this case:
- For a successful long hit, the expected value of X is
- Conversely, if the long hit isn't successful, the expected value of X becomes
We also know that the likelihood of succeeding with a long hit is
Consequently, the chance of failure in a long hit is
Thus, the expected value of X when opting for the long hit strategy is:
In the first part of this question, we calculated the expected value using the short hit strategy, yielding:
Given that the expected value for X is smaller (which is better) when utilizing the short hit option, we can conclude that this approach is superior.