Gary’s is a small publishing company that publishes math books. The production costs include a one-time cost for editing the boo
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Answer:
- f(x) = 34.59 +3.74x
- 0.96
- very strong
- 8.93
Step-by-step explanation:
1. The selection of answers offers a choice of positive or negative slope, a slope of about 4 or about 35, and y-intercepts from the same set of values.
If you consider a couple of points (at the ends of the domain is usually a good choice), you see the slope is about 4 and the y-intercept is around 30.
For example, the points (5, 50) and (15, 91) have a slope of (91-50)/(15-5) = 4.1 so will give rise to the equation ...
y -50 = 4.1(x -5)
Filling in x=0 gives y = 50 -20.5 = 29.5
So, the nearest of the offered choices is ...
f(x) = 34.59 +3.74x
Please note that no calculator is involved. We simply estimated the parameters of the regression line based on a couple of the data points. This estimate is sufficient to allow us to find the correct answer choice.
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2. If we look at a few other data points, we see that they have a generally upward trend that matches the above equation pretty well. That suggests a very high value of correlation, so the appropriate choices would be 0.93 or 0.96. Of course, the correlation is positive, matching the sign of the slope of the regression line. (Since the data points do not fall exactly on a line, the correlation is not 1.00. My assessment is they fall close enough to the line to rate a correlation of .96 instead of .93.)
At this point, the output of your calculator can confirm that the correlation coefficient is closer to 0.96. Mine says r = 0.9624.
r = 0.96
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3. We have already determined by examining the data points that the correlation is "very strong." The correlation coefficient of 0.96 confirms this.
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4. Using the equation of part 1, we can find the number of study hours:
68 = 34.59 +3.74x
(68 -34.59)/3.74 = x ≈ 8.933
We expect a score of 68 is associated with about 8.93 study hours.
_____
Please note that we have used very little calculation to determine the answers to this question. The only requirement is a general understanding of what linear regression and correlation coefficients mean.
Answer:
Part a: <em>The probability of no arrivals in a one-minute period is 0.000045.</em>
Part b: <em>The probability of three or fewer passengers arrive in a one-minute period is 0.0103.</em>
Part c: <em>The probability of no arrivals in a 15-second is 0.0821.</em>
Part d: <em>The probability of at least one arrival in a 15-second period is 0.9179.</em>
Step-by-step explanation:
Airline passengers are arriving at an airport independently. The mean arrival rate is 10 passengers per minute. Consider the random variable X to represent the number of passengers arriving per minute. The random variable X follows a Poisson distribution. That is,
The probability mass function of X can be written as,
Substitute the value of λ=10 in the formula as,
Part a:
The probability that there are no arrivals in one minute is calculated by substituting x = 0 in the formula as,
<em>The probability of no arrivals in a one-minute period is 0.000045.</em>
Part b:
The probability mass function of X can be written as,
The probability of the arrival of three or fewer passengers in one minute is calculated by substituting \lambda = 10λ=10 and x = 0,1,2,3x=0,1,2,3 in the formula as,
<em>The probability of three or fewer passengers arrive in a one-minute period is 0.0103.</em>
Part c:
Consider the random variable Y to denote the passengers arriving in 15 seconds. This means that the random variable Y can be defined as
That is,
So, the probability mass function of Y is,
The probability that there are no arrivals in the 15-second period can be calculated by substituting the value of (λ=2.5) and y as 0 as:
<em>The probability of no arrivals in a 15-second is 0.0821.</em>
Part d:
The probability that there is at least one arrival in a 15-second period is calculated as,
<em>The probability of at least one arrival in a 15-second period is 0.9179.</em>
Step-by-step explanation:
We know that,
Where,
X = raw score = 84
μ = mean = 68
σ = standard deviation = 10
Putting the values,
The percent of his sales that were less than or equal to 84 inches, is
Therefore, the remaining 100-94.5=5.5% were more than 84 inches.