Question

In: Statistics and Probability

in a survey of 255 athletes it was found that 122 owned a convertible, 104 owned...

in a survey of 255 athletes it was found that 122 owned a convertible, 104 owned a big screen tv and 117 owned a sporting goods store. 26 owned a convertible and a store; 36 owned a tv and a store and 64 owned a convertible and a tv. 12 owned all 3.

A. how many owned a convertible or tv?
B. how many owned a convertible and a tv but not a store.
C. how many did not own any of the three?
D. how many owned exactly one item in the survey?
E. how many owned a tv or store but not a convertible?

Solutions

Expert Solution

The problem can be solved using Venn Diagram Approach

Here,

a = Athletes owning a convertible only

b = Athletes owning a big screen tv only

c = Athletes owning a sporting good store only

g = Athletes owning a convertible and big screen tv and sporting good store

d+g = Athletes owning a convertible and sporting good store

g+e = Athletes owning a big screen tv and sporting good store

f+g = Athletes owning a convertible and big screen tv

Given Information:

g = 12

f+g = 64

g+e = 36

d+g = 26

a+d +g +f = 122 (Athletes owning a convertible)

b +f + g + e = 104 (Athletes owning a big screen tv)

c +d +g + e = 117 ( Athletes owning a sporting goods store)

From the above equations,

g = 12 , f = 52 , e = 24 , d = 14 , a = 44 , b =16, c =67

A. Athletes owned a convertible or TV

Total number of athletes owning a convertible or TV = 44+52+16+14+12+24 = 162

B) Athletes owning a convertible and TV but not a store

Total number of athletes owning a Convertible or TV = 52

C) Athletes owning exactly one item in the survey

Total athletes owning exactly one item = 44 + 67 + 16 = 127

D) Athletes owning a tv or store but not convertible

Total Athletes owning a big screen tv or a store = 67 + 24 + 16 = 107

orchestra answered 2 years ago
Next > < Previous

Related Solutions

In a survey of​ four-year colleges and​ universities, it was found that 255 offered a liberal...
In a survey of​ four-year colleges and​ universities, it was found that 255 offered a liberal arts degree. 110 offered a computer engineering degree. 481 offered a nursing degree. 30 offered a liberal arts degree and a computer engineering degree. 211 offered a liberal arts degree and a nursing degree. 86 offered a computer engineering degree and a nursing degree. 25 offered a liberal arts​ degree, a computer engineering​ degree, and a nursing degree. 33 offered none of these degrees....
In a survey of​ four-year colleges and​ universities, it was found that 255 offered a liberal...
In a survey of​ four-year colleges and​ universities, it was found that 255 offered a liberal arts degree. 110 offered a computer engineering degree. 481 offered a nursing degree. 30 offered a liberal arts degree and a computer engineering degree. 211 offered a liberal arts degree and a nursing degree. 86 offered a computer engineering degree and a nursing degree. 25 offered a liberal arts​ degree, a computer engineering​ degree, and a nursing degree. 33 offered none of these degrees....
In a survey of​ four-year colleges and​ universities, it was found that 255 offered a liberal...
In a survey of​ four-year colleges and​ universities, it was found that 255 offered a liberal arts degree. 110 offered a computer engineering degree. 481 offered a nursing degree. 30 offered a liberal arts degree and a computer engineering degree. 211 offered a liberal arts degree and a nursing degree. 86 offered a computer engineering degree and a nursing degree. 25 offered a liberal arts​ degree, a computer engineering​ degree, and a nursing degree. 33 offered none of these degrees....
Suppose in a survey of n = 400 students, 255 responded that they prefer small classes...
Suppose in a survey of n = 400 students, 255 responded that they prefer small classes and 145 responded that they prefer large classes. Let p denote the fraction of all students who preferred small classes at the time of the survey, and ^ p be the fraction of survey respondents who preferred small classes. (Hint: X is distributed as a Bernoulli random variable) 1.Use the survey result to estimate p, and calculate the standard error of your estimator. (Hint:...
Question 12 pts (CO 1) A survey of 1272 pre-owned vehicle shoppers found that 8% bought...
Question 12 pts (CO 1) A survey of 1272 pre-owned vehicle shoppers found that 8% bought the extended warranties. What is the population and what is the sample? Group of answer choices Population: pre-owned vehicle shoppers; Sample: the 8% that bought extended warranties Population: 1272 pre-owned vehicle shoppers; Sample: the 8% that bought extended warranties Population: pre-owned vehicle shoppers; Sample: 1272 pre-owned vehicle shoppers Population: 1272 pre-owned vehicle shoppers; Sample: pre-owned vehicle shoppers Question 22 pts (CO 1) A survey...
When 328 college students are randomly selected and surveyed, it is found that 122 own a...
When 328 college students are randomly selected and surveyed, it is found that 122 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car. A) 0.328 < p < 0.416 B) 0.320 < p < 0.424 C) 0.310 < p < 0.434 D) 0.303 < p < 0.441
A market research company conducted a telephone survey of 255 Melbourne households to determine the proportion...
A market research company conducted a telephone survey of 255 Melbourne households to determine the proportion of households seeking to purchase a new car in the next two years. An interval estimate of 0.151 to 0.289 was calculated. Determine the level of confidence (answer as percentage correct to two decimal places).
122. Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback...
122. Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in the previous month. The results are summarized in the Table 2.83. # of books Freq. Relative Freq. 0 18    1 24 2 24 3 22 4 15 5 10 7 5 9 1 a. Are there any outliers in the data? Use an appropriate numerical test involving the IQR to identify outliers, if any, and clearly state your...
On January 1, 2017, Olson Corporation issued $6 million of 10-year, 7%, convertible debentures at 104....
On January 1, 2017, Olson Corporation issued $6 million of 10-year, 7%, convertible debentures at 104. Investment bankers believe that the debenture would have sold at 102 without the conversion privilege. Interest is to be paid semi-annually on June 30 and December 31. Each $1,000 debenture can be converted into five common shares of Olson after December 31, 2018. On January 1, 2016, $400,000 of debentures is converted into common shares, and on March 31, 2019, an additional $400,000 of...
(Survey from 9.41: In a survey of 446 students, it was found that 50% of the...
(Survey from 9.41: In a survey of 446 students, it was found that 50% of the sampled students lived on campus and 50% lived off campus.) In the same survey used in 9.41, 88% of the sampled students were right-handed. a. The proportion of all people who are right-handed is said to be 0.88. Tell the value of standardized sample proportion z, if we want to test whether the proportion of all students who are right- handed could be 0.88....
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT