Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
9th Edition
ISBN: 9781337515429
Author: GRAVETTER
Publisher: Cengage
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Chapter 5.3, Problem 4LC
To determine
To find: The mean and standard deviation for sample.
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Question 3
The following stem-and-leaf displays the weekly salary of employees at this firm.
Stem-and-Leaf Display
Leaf Unit = 10.0
N=x
5
3 00123
12 4 0125888
(y)
5 11234456777
z
6 13568
5
7 154
2
8 46
i.
Determine the value of x, y and z.
[3]
ii. What is the value of the median?
[2]
iii.
Find the mode of this data set.
iv.
Calculate the range
[1]
[2]
Let Y be a continuous RV with PDF
otherwise
Find the CDF, Fry), of Y .
Find an expression for pth, p € (0, 1), quantile of the distribution.
Find E(Y) and V(Y).
Find E(-2Y + 1) and V(-3Y - 2).
Find E(Y3).
Let X be a continuous RV with CDF
Find P(X < 0), P(-1 < X < 1) and P(0.5 < X).
Based on your answers to the above questions, what is the median of the distribu-tion? Why
Find the PDF, fx (x), of X.
Chapter 5 Solutions
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Ch. 5.2 - What location in a distribution corresponds to z =...Ch. 5.2 - For a population with = 80 and = 12, what is the...Ch. 5.2 - For a sample with M 72and s 4, what is the X...Ch. 5.3 - In a population with = 60. a score of X = 58...Ch. 5.3 - In a sample with a standard deviation of s = 8, a...Ch. 5.3 - Prob. 3LCCh. 5.3 - Prob. 4LCCh. 5.4 - Prob. 1LCCh. 5.4 - A sample with a mean of M = 50 and a standard...Ch. 5.4 - Which of the following is an advantage of...
Ch. 5.4 - Last week Sarah had exams in math and in Spanish....Ch. 5.5 - A set of scores has a mean of = 63 and a standard...Ch. 5.5 - A distribution with = 35 and = 8 is being...Ch. 5.5 - Using z-scores, a sample with M = 37 and s = 6 is...Ch. 5.6 - For the past 20 years, the high temperature on...Ch. 5.6 - A Score of X = 73 is obtained from a population....Ch. 5.6 - Under what circumstances would a score that is 15...Ch. 5 - Explain how a z-score identifies an exact location...Ch. 5 - For a population with a standard deviation of =...Ch. 5 - For a sample with a standard deviation of s = 12....Ch. 5 - For a population with = 40 and = 8: a. Find the...Ch. 5 - For a population with = 80 and = 9. find the...Ch. 5 - A sample has a mean of M = 90 and a standard...Ch. 5 - A sample has a mean of M =60 and a standard...Ch. 5 - R. Fine the-. z-score corresponding to a |score of...Ch. 5 - Fine the x value corresponding to z. - 0.75 for of...Ch. 5 - Find the z-score corresponding to X 40 and the X...Ch. 5 - Find the e-score corresponding to X = 24 and the X...Ch. 5 - A score that is 12 points below the mean...Ch. 5 - A score that is 20 points above the mean...Ch. 5 - For a population with a standard deviation of =...Ch. 5 - For a population with a mean of = 45, a score of...Ch. 5 - For a sample with a standard deviation of s 6, a...Ch. 5 - For a sample with a mean of M - 63, a score of X =...Ch. 5 - In a population distribution, a score of X = 57...Ch. 5 - In a sample distribution, a score of V 21...Ch. 5 - A distribution of exam scores has a mean of = 42....Ch. 5 - For each of the following, identify the exam score...Ch. 5 - A population with a mean of = 41 and a standard...Ch. 5 - A sample with a mean of M = 62 and a standard...Ch. 5 - A population consists of the following N 6...Ch. 5 - A sample consists of the Following n = 5 scores:...Ch. 5 - For each of the following populations, would a...
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- A survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forwardLet X be a continuous RV with PDF where a > 0 and 0 > 0 are parameters. verify that f-∞ /x (x)dx = 1. Find the CDF, Fx (7), of X.arrow_forward6. [20] Let X be a continuous RV with PDF 2(1), 1≤x≤2 fx(x) = 0, otherwisearrow_forward
- A survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forwardA survey of 581 citizens found that 313 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? Enter the result as a decimal rounded to 3 decimal digits. Your Answer:arrow_forward2. The SMSA data consisting of 141 observations on 10 variables is fitted by the model below: 1 y = Bo+B1x4 + ẞ2x6 + ẞ3x8 + √1X4X8 + V2X6X8 + €. See Question 2, Tutorial 3 for the meaning of the variables in the above model. The following results are obtained: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.302e+03 4.320e+02 3.015 0.00307 x4 x6 x8 x4:x8 x6:x8 -1.442e+02 2.056e+01 -7.013 1.02e-10 6.340e-01 6.099e+00 0.104 0.91737 -9.455e-02 5.802e-02 -1.630 0.10550 2.882e-02 2.589e-03 11.132 1.673e-03 7.215e-04 2.319 F) x4 1 3486722 3486722 17.9286 4.214e-05 x6 1 14595537 x8 x4:x8 x6:x8 1 132.4836 < 2.2e-16 1045693 194478 5.3769 0.02191 1 1198603043 1198603043 6163.1900 < 2.2e-16 1 25765100 25765100 1045693 Residuals 135 26254490 Estimated variance matrix (Intercept) x4 x6 x8 x4:x8 x6:x8 (Intercept) x4 x6 x8 x4:x8 x6:x8 0.18875694 1.866030e+05 -5.931735e+03 -2.322825e+03 -16.25142055 0.57188953 -5.931735e+03 4.228816e+02 3.160915e+01 0.61621781 -0.03608028 -0.00445013 -2.322825e+03…arrow_forward
- In some applications the distribution of a discrete RV, X resembles the Poisson distribution except that 0 is not a possible value of X. Consider such a RV with PMF where 1 > 0 is a parameter, and c is a constant. (a) Find the expression of c in terms of 1. (b) Find E(X). (Hint: You can use the fact that, if Y ~ Poisson(1), the E(Y) = 1.)arrow_forwardSuppose that X ~Bin(n,p). Show that E[(1 - p)] = (1-p²)".arrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forward
- I need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forwardThis exercise is based on the following data on four bodybuilding supplements. (Figures shown correspond to a single serving.) Creatine(grams) L-Glutamine(grams) BCAAs(grams) Cost($) Xtend(SciVation) 0 2.5 7 1.00 Gainz(MP Hardcore) 2 3 6 1.10 Strongevity(Bill Phillips) 2.5 1 0 1.20 Muscle Physique(EAS) 2 2 0 1.00 Your personal trainer suggests that you supplement with at least 10 grams of creatine, 39 grams of L-glutamine, and 90 grams of BCAAs each week. You are thinking of combining Xtend and Gainz to provide you with the required nutrients. How many servings of each should you combine to obtain a week's supply that meets your trainer's specifications at the least cost? (If an answer does not exist, enter DNE.) servings of xtend servings of gainzarrow_forwardI need help with this problem and an explanation of the solution for the image described below. (Statistics: Engineering Probabilities)arrow_forward
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