Question

In a poll conducted by the General Social Survey, 81% of respondents said their jobs were sometimes or always stressful. You choose a sample of 10 respondents. Answer the following questions about binomial probabilities. Use Excel to show your work.

Show work in Excel.

1. What constitutes "success" in this problem? What is the probability of success? Of failure?

2.  Construct a probability distribution and its graph.

3. Determine the following probabilities

P(x = 7)

P(x <5)

P(x > 8)

P(3 < x < 6)

4. What is the mean and standard deviation of this distribution?

Answer 1

Ans:

1)Success is to respond that jobs were sometimes or always stressful

Probability of success,p=0.81

Probability of failure,1-p=1-0.81=0.19

2)Binomial distribution with n=10 and p=0.81

P(x=k)=10Ck*0.81^k*(1-0.81)^10-k

x	P(x)
0	0.0000
1	0.0000
2	0.0001
3	0.0006
4	0.0043
5	0.0218
6	0.0773
7	0.1883
8	0.3010
9	0.2852
10	0.1216

3)

P(x=7)=binomdist(7,10,0.81,false)=0.1883

P(x<5)=P(x<=4)=binomdist(4,10,0.81,true)=0.0049

P(x>8)=1-P(x<=8)=1-binomdist(8,10,0.81,true)=0.4068

P(3<x<6)=P(x=4)+P(x=5)=binomdist(4,10,0.81,false)+binomdist(5,10,0.81,false)=0.0260

4)

mean=np=10*0.81=8.1

standard deviation=sqrt(10*0.81*(1-0.81))=1.24