Question

In: Statistics and Probability

Stress at work: In a poll about work, 84% of respondents said that their jobs were...

Stress at work: In a poll about work, 84% of respondents said that their jobs were sometimes or always stressful. Twelve workers are chosen at random. Round the answers to four decimal places.

(a) What is the probability that exactly 11 of them find their jobs stressful?

(b) What is the probability that more than 9 find their jobs stressful?

(c) What is the probability that fewer than 6 find their jobs stressful?

(d) Would it be unusual if fewer than 5 of them find their jobs stressful?

Solutions

Expert Solution

Use excel formula " =BINOM.DIST(x, n ,p, FALSE) "

=BINOM.DIST(x, 12, 0.84, FALSE) Where, x=0,1,2....12

x Excel formula P(X=x)
0 =BINOM.DIST(x, 12, 0.84, FALSE) 0.0000
1 =BINOM.DIST(1, 12, 0.84, FALSE) 0.0000
2 =BINOM.DIST(2, 12, 0.84, FALSE) 0.0000
3 =BINOM.DIST(3, 12, 0.84, FALSE) 0.0000
4 =BINOM.DIST(4, 12, 0.84, FALSE) 0.0001
5 =BINOM.DIST(5, 12, 0.84, FALSE) 0.0009
6 =BINOM.DIST(6, 12, 0.84, FALSE) 0.0054
7 =BINOM.DIST(7, 12, 0.84, FALSE) 0.0245
8 =BINOM.DIST(8, 12, 0.84, FALSE) 0.0804
9 =BINOM.DIST(9, 12, 0.84, FALSE) 0.1876
10 =BINOM.DIST(10, 12, 0.84, FALSE) 0.2955
11 =BINOM.DIST(11, 12, 0.84, FALSE) 0.2821
12 =BINOM.DIST(12, 12, 0.84, FALSE) 0.1234

------------------------------------------------------------------------------------------------------------

------------------------------------------------------------------------------------------------------------

------------------------------------------------------------------------------------------------------------

It be unusual if fewer than 5 of then find their jobs stressful, since the probability is

Since the probability 0.0001 is less than 0.05. Therefore it is considered unusual.


Related Solutions

In a poll conducted by the General Social Survey, 79% of respondents said that their jobs...
In a poll conducted by the General Social Survey, 79% of respondents said that their jobs were sometimes or always stressful. Two hundred workers are chosen at random. Use the TI-84 Plus calculator as needed. Round your answer to at least four decimal places. (a) Approximate the probability that 165 or fewer workers find their jobs stressful. (b) Approximate the probability that more than 158 workers find their jobs stressful. (c) Approximate the probability that the number of workers who...
In a poll 1040 of 2260 respondents said they would prefer to live somewhere else. Confirm...
In a poll 1040 of 2260 respondents said they would prefer to live somewhere else. Confirm the distribution for p-hat is approximately normal and find a 95% confidence interval for the proportion of people who prefer to live somewhere else.
In a poll, respondents were asked whether they had ever been in a car accident.
Find the indicated probability. In a poll, respondents were asked whether they had ever been in a car accident. 473 respondents indicated that they had been in a car accident and 243 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident?
1. Presume that the following data were collected from respondents to a poll asking for their...
1. Presume that the following data were collected from respondents to a poll asking for their rating of the current state of the economy, ranging from 1 to 100 (1= worst, 100 = best). Party affiliation Republican Independent Democrat M 45 41 31 s 9.1 8.7 10.3 n 15 13 19 1). State your hypotheses for the effect of party affiliation:       H0:       H1: 2). Test your hypothesis using a one-way ANOVA. Show all your work andenter your information...
Respondents in the 2017 General Social Survey (GSS) were asked “on an average work day, about...
Respondents in the 2017 General Social Survey (GSS) were asked “on an average work day, about how many hours do you have to relax or pursue the activities that you enjoy?”. 244 males responded to the question and 262 females responded. Men reported an average of 3.28 hours per day (with a standard deviation of 2.12 hours) and women reported an average of 2.99 hours per day (sd=2.05). A. Calculate and interpret the 95% confidence interval for relaxation hours for...
In a recent survey about US policy in Iraq, 62 % of the respondents said that...
In a recent survey about US policy in Iraq, 62 % of the respondents said that they support US policy in Iraq. Females comprised 53% of the sample, and of the females, 46% supported US policy in Iraq. A person is selected at random. What is the probability that the person we select is female and supports U.S. policy in Iraq? Are the events "does not support U.S, policy in Iraq" and "female" statistically independent? Why or why not? What...
1. From a recent poll in which respondents were asked if they felt that U.S. nuclear...
1. From a recent poll in which respondents were asked if they felt that U.S. nuclear weapons made them feel safer, 550 out of 1000 people said “no.” a) Find the sample proportion, ?̂, of people who responded “no”. Use the appropriate formula and show your work. b) Find the margin of error for a 95% confidence interval for the true population proportion of people who feel that U.S. nuclear weapons do not make them feel safer. Round to three...
A public opinion poll surveyed a simple random sample of 1000 voters. Respondents were classified by...
A public opinion poll surveyed a simple random sample of 1000 voters. Respondents were classified by gender (male or female) and by voting preference (Republican, Democrat, or Independent). Results are shown in the contingency table below.                                                 VOTING PREFERENCES                                                 Rep        Dem      Ind         Row Total Male                                      350         075         25           450 Female                                 275         240         35           550 Column Total                     625         315         60           1000 Is there a gender gap? D3 the men's voting preferences differ significantly from the women's preferences? Use...
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll,...
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1000and x=557 who said "yes". Use a 90%confidence level. A) Find the best point estimate of the population P. (Round to three decimal places as needed) B) Identify the value of margin of error E. ________ (Round to four decimal places as needed) C) Construct a confidence interval. ___ < p <. (Round to three decimal places as needed) D) Write a statement that...
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll...
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll of 968 randomly selected American adults, 511 of them responded with “yes.” a). Find the 95% confidence interval for the proportion of adults who felt vulnerable to identify theft . b). Write a statement that correctly interprets the confidence interval. Choose the correct answer below. A. One has 95% confidence that the sample proportion is equal to the population proportion. B. One has 95%...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT