Use the table and the data provided to analyze the following data. During gym class, the pulse rate was recorded for 19 students
before and after an exercise warm-up. The pulse rates are listed below. Pulse before Exercise Pulse after Exercise 67 87 67 88 67 89 68 89 71 91 72 93 72 93 75 95 77 96 77 97 79 98 81 98 85 101 87 105 87 105 91 119 97 125 103 125 121 147 Part A: Create a stemplot for each set of data. Justify your reasoning for split or nonsplit stems. (10 points) Part B: Compare and contrast the two data sets. Justify your answer using key features of the data (shape, outliers, center, and spread). (10 points) just a little confused on how to set it up
1 answer:
Answer:
Part A
Please see attached the required stem and leaf plot
For the stem and leaf plot, the nonsplit system is used because of clarity for analysis
Part B:
From the shape of the stem and leaf plot we have that there is an average increase of pulse rate of 20 pulses in all the 19 students after the exercise
The shape of the plot is relatively the same for the before and after exercise save for the decrease in the third to the last row by one and the increase in the second to the last roe by one student
The spread remained relatively constant in both cases with the most being in the 60s range having 7 students in the before exercise and the 80s range having 8 students in the after exercise leaf plot.
Step-by-step explanation:
The given data are;
67 87
67 88
67 89
68 89
71 91
72 93
72 93
75 95
77 96
77 97
79 98
81 98
85 101
87 105
87 105
91 119
97 125
103 125
121 147
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Answer:
a. 61.5%; b. About 61.8%; c. About 36.4%
Step-by-step explanation:
This is a kind of question that we can solve using the Bayes' Theorem. We have here all the different conditional probabilities we need to solve this problem.
According to that theorem, the probability of a selected product attains a good review is:
(1)
In words, the probability that a selected product attains a <em>good review</em> is an <em>event </em>that depends upon the sum of the conditional probabilities that the product comes from <em>high successful product</em> P(G|H) by the probability that this product is a <em>highly successful product</em> P(H), plus the same about the rest of the probabilities, that is, P(G|M)*P(M) or the probability that the product has a good review coming from a <em>moderately successful</em> product by the probability of being moderately successful, and a good review coming from a poor successful product by the probability of being poor successful or P(G|P)*P(P).
<h3>The probability that a randomly selected product attains a good review</h3>In this way, the probability that a randomly selected product attains a good review is the result of the formula (1). Where (from the question):
P(G|H) = 95% or 0.95 (probability of receiving a good review being a highly successful product)
P(G|M) = 60% or 0.60 (probability of receiving a good review being a moderately successful product)
P(G|P) = 10% or 0.10 (probability of receiving a good review being a poorly successful product)
P(H) = 40% or 0.40 (probability of being a highly successful product).
P(M) = 35% or 0.35 (probability of being a moderately successful product).
P(P) = 25% or 0.25 (probability of being a poor successful product).
Then,
That is, <em>the probability that a randomly selected product attains a good review</em> is 61.5%.
<h3>The probability that a new product attains a good review is a highly successful product</h3>We are looking here for P(H|G). We can express this probability mathematically as follows (another conditional probability):
We can notice that the probability represents a fraction from the probability P(G) already calculated. Then,
Then, the probability of a product that attains a good review is indeed a highly successful product is about 0.618 or 61.8%.
<h3>The probability that a product that <em>does not attain </em>a good review is a moderately successful product</h3>The probability that a product does not attain a good review is given by a similar formula than (1). However, this probability is the complement of P(G). Mathematically:
P(NG|H) = 1 - P(G|H) = 1 - 0.95 = 0.05
P(NG|M) = 1 - P(G|M) = 1 - 0.60 = 0.40
P(NG|P) = 1 - P(G|M) = 1 - 0.10 = 0.90
So
Which is equal to
P(NG) = 1 - P(G) = 1 - 0.615 = 0.385
Well, having all this information at hand:
Then, the <em>probability that a new product does not attain a good review and it is a moderately successful product is about </em>0.364 or 36.4%.