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In: Statistics and Probability

A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical...

A survey on British Social Attitudes asked respondents if they had ever boycotted goods for ethical reasons (Statesman, January 28, 2008). The survey found that 23% of the respondents have boycotted goods for ethical reasons.

In a sample of six British citizens, what is the probability that two have ever boycotted goods for ethical reasons?
In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?
In a sample of ten British citizens, what is the probability that between 3 and 6 have boycotted goods for ethical reasons?
In a sample of ten British citizens, what is the expected number of people that have boycotted goods for ethical reasons? Also find the standard deviation.

Solutions

Expert Solution

It is given that

Percentage of respondents who have boycotted goods for ethical reasons=23%. Let us call it p which is the probability of a British citizen who boycotted goods for ethical reasons:

There are only two possible outcomes of a British citizen ie eith boycott or not boycott.

p=0.23 q=1-p =0.77

a. In a sample of six British citizens,the probability that two have ever boycotted goods for ethical reasons?

Here n=6 , r=2 in a Binomial distribution.

Therfore the probability that two have ever boycotted goods for ethical reasons

b. In a sample of six British citizens, what is the probability that at least two respondents have boycotted goods for ethical reasons?

Here again, n=6, p=0.23, q=0.77. Out of six, at least two have boycotted means 2 or more ie

SInce we know that the total probability is 1 and hence

c.In a sample of ten British citizens, what is the probability that between 3 and 6 have boycotted goods for ethical reasons?

Here n=10. Between 3 and 6 have boycotted goods means x=3,4,5 and 6 and teh required probability is theerfore

d.In a sample of ten British citizens, what is the expected number of people that have boycotted goods for ethical reasons? Also find the standard deviation.

We have here n=10, p=0.23 and 1-p=0.77. We also know that for a bionomial distribution, the mean=expected number of people that have boycotted goods =np

We also know that the variance

Also we know that

orchestra answered 1 year ago

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