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STATISTICS AND PROBABILITY
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Recent questions in Statistics and Probability
Modeling data distributions
asked 2021-03-18
a) To calculate: The least squares regression line for the data points using the table given below. \begin{array}{|c|c|} \hline Fertilizer & x & 100 & 150 & 200 & 250 \\ \hline Yield & y & 35 & 44 & 50 & 56 \\ \hline \end{array} b)To calculate: The approximate yield when 175 pounds of fertizers were used per acre of land.
Random variables
asked 2021-03-18
A population of values has a normal distribution with
\(\displaystyle\mu={133.5}\)
and
\(\displaystyle\sigma={5.2}\)
. You intend to draw a random sample of size
\(\displaystyle{n}={230}\)
.
Find the probability that a single randomly selected value is between 133.6 and 134.1.
\(\displaystyle{P}{\left({133.6}{<}{X}{<}{134.1}\right)}=\)
?
Write your answers as numbers accurate to 4 decimal places.
Two-way tables
asked 2021-03-12
Baseball star David Ortiz-nicknamed "Big Papi"-is known for his ability to deliver hits in high-pressure situations. Here is a two-way table of his hits, walks, and outs in all of his regular-season and post-season plate appearances from 1997 through 2014. Choose a plate appearance at random. Are the events "Hit" and "Post-season" independent? Justify your answer.
Confidence intervals
asked 2021-03-12
Do piano lessons improve the spatial-temporal reasoning of preschool children? A study designed to investigate this question measured the spatial-temporal reasoning of a random sample of 34 preschool children before and after 6 months of piano lessons. The differences (After - Before) in the reasoning scores have mean 3.618 and standard deviation 3.055.
Comparing two groups
asked 2021-03-12
The mean + 1 sd of In [calcium intake (mg)] among 25 females, 12 to 14 years of age, below the poverty level is
\(6.56 + 0.64.\)
Similarly, the mean + 1 sd of In [calcium intake (mg)] among 40 females, 12 to 14 years of age, above the poverty level is
\(6.80 + 0.76.\)
8.2 Test for a significant difference between the variances of the two groups.
8.3 What is the appropriate procedure to test for a signifi- cant difference in means between the two groups?
8.4 Implement the procedure in Problem 8.3 using the critical-value method.
8.5 What is the p-value corresponding to your answer to Problem 8.4?
8.6 Compute a
\(95\%\)
Cl for the difference in means between the two groups.
Analyzing categorical data
asked 2021-03-12
Is the mode the measure of central tendency that is best used with a skewed distribution?
Analyzing categorical data
asked 2021-03-12
For each of the following variables, indicate whether they are categorical or numerical. Also, write down what type of graph can be drawn for each.
a) Position of a university staff members.
b) Weight of participants.
C Air temperature on the Celsius scale
D) The daily number of code lines written by a programmer
Summarizing quantitative data
asked 2021-03-12
Describe the summary of the perfomance of eight graders nationwide.
Modeling data distributions
asked 2021-03-11
An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds per square inch) and mileage (in thousands of miles). A mathematical model for the data is given by
\(\displaystyle f{{\left({x}\right)}}=-{0.554}{x}^{2}+{35.5}{x}-{514}.\)
\(\begin{array}{|c|c|} \hline x & Mileage \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}\)
(A) Complete the table below.
\(\begin{array}{|c|c|} \hline x & Mileage & f(x) \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}\)
(Round to one decimal place as needed.)
\(A. 20602060xf(x)\)
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,45), (30,51), (32,56), (34,50), and (36,46). A parabola opens downward and passes through the points (28,45.7), (30,52.4), (32,54.7), (34,52.6), and (36,46.0). All points are approximate.
\(B. 20602060xf(x)\)
Acoordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2.
Data points are plotted at (43,30), (45,36), (47,41), (49,35), and (51,31). A parabola opens downward and passes through the points (43,30.7), (45,37.4), (47,39.7), (49,37.6), and (51,31). All points are approximate.
\(C. 20602060xf(x)\)
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,45), (45,51), (47,56), (49,50), and (51,46). A parabola opens downward and passes through the points (43,45.7), (45,52.4), (47,54.7), (49,52.6), and (51,46.0). All points are approximate.
\(D.20602060xf(x)\)
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,30), (30,36), (32,41), (34,35), and (36,31). A parabola opens downward and passes through the points (28,30.7), (30,37.4), (32,39.7), (34,37.6), and (36,31). All points are approximate.
(C) Use the modeling function f(x) to estimate the mileage for a tire pressure of 29
\(\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\)
and for 35
\(\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\)
The mileage for the tire pressure
\(\displaystyle{29}\frac{{{l}{b}{s}}}{{{s}{q}}}\in.\)
is
The mileage for the tire pressure
\(\displaystyle{35}\frac{{{l}{b}{s}}}{{{s}{q}}}\)
in. is
(Round to two decimal places as needed.)
(D) Write a brief description of the relationship between tire pressure and mileage.
A. As tire pressure increases, mileage decreases to a minimum at a certain tire pressure, then begins to increase.
B. As tire pressure increases, mileage decreases.
C. As tire pressure increases, mileage increases to a maximum at a certain tire pressure, then begins to decrease.
D. As tire pressure increases, mileage increases.
Confidence intervals
asked 2021-03-11
The local energy company claims the average annual electricity bill for its subscribers is just $600. A consumer watchdog group wants to dispute this claim. All agree that the standard deviation sigma of annual electricity bills is $150.
Some time later, a wealthy activist provides funding for a simple random sample of 250 households. The average annual electricity bill for this sample is $622. Find a
\(95\%\)
confidence interval for the true mean annual electric bill, based on this sample.
Alternate coordinate systems
asked 2021-03-11
Convert the point from spherical coordinates to rectangular coordinates.
\((9, \pi, \frac{\pi}{2})\)
\((x, y, z) = ?\)
Confidence intervals
asked 2021-03-11
Let
\(f(x)=4−\frac{2}{x}+\frac{6}{x^{2}}\)
.
Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).
f is increasing on the intervals
f is decreasing on the intervals
The relative maxima of f occur at x =
The relative minima of f occur at x =
Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none".
In the last two, your answer should be a comma separated list of x values or the word "none".
Modeling data distributions
asked 2021-03-11
Let's say the widget maker has developed the following table that shows the highest dollar price p. widget where you can sell N widgets. Number N Price p
\(200 53.00\)
\(250 52.50\)
\(300 52.00\)
\(35051.50\)
(a) Find a formula for pin terms of N modeling the data in the table. (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in month as a function of the number N of widgets produced in a month.
\(R=\)
Is Ra linear function of N? (c) On the basis of the tables in this exercise and using cost,
\(C= 35N + 900\)
, use a formula to express the monthly profit P, in dollars, of this manufacturer asa function of the number of widgets produced in a month
\(p=\)
(d) Is Pa linear function of N2 e. Explain how you would find breakeven. What does breakeven represent?
Sampling distributions
asked 2021-03-11
1) Describe sampling distributions and sampling variavility
2) Explain The Central Limit Theorem
3) Explain how confidence intervals are created and what can they tell us about population parameters
Confidence intervals
asked 2021-03-09
Calculate confidence intervals for ratio of two population variances and ratio of standard deviations. Assume that samples are simple random samples and taken from normal populations. a)
\(\displaystyle\alpha={0.05},\ {n}_{{{1}}}={30},\ {s}_{{{1}}}={16.37},\ {n}_{{{2}}}={39},\ {s}_{{{2}}}={9.88}\)
b)
\(\displaystyle\alpha={0.01},\ {n}_{{{1}}}={25},\ {s}_{{{1}}}={5.2},\ {n}_{{{2}}}={20},\ {s}_{{{2}}}={6.8}\)
Confidence intervals
asked 2021-03-09
In a study of the accuracy of fast food drive-through orders, Restaurant A had 298 accurate orders and 51 that were not accurate. a. Construct a 90% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part (a) to this 90% confidence interval for the percentage of orders that are not accurate at Restaurant B:
\(\displaystyle{0.127}{<}{p}{<}{0.191}\)
. What do you conclude? a. Construct a 90% confidence interval. Express the percentages in decimal form. ___
Random variables
asked 2021-03-09
A distribution of values is normal with a mean of 203.8 and a standard deviation of 50.2.
Find the probability that a randomly selected value is less than 113.4.
\(\displaystyle{P}{\left({X}{<}{113.4}\right)}=\)
?
Write your answers as numbers accurate to 4 decimal places.
Comparing two groups
asked 2021-03-09
Decide equation using only factors to solve this problem
\(12x^{2}\ +\ 5x\ -\ 2 = 0\)
Modeling data distributions
asked 2021-03-09
Define the term Mean.
Analyzing categorical data
asked 2021-03-09
Why is hair color classified as categorical data?
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