A survey of over 20,000 U.S. high school students revealed that 10% of the stude

Question

A survey of over 20,000 U.S. high school students revealed that 10% of the students say that they stole something from a store in the past year. This is down 7% from the last survey, which was performed two years earlier. You decide to take a random sample of 10 high school students from your city and ask them this question.

(a) What is the mean number (±0.0001) of students in your sample who say that they stole something from a store in the past year?

=

(b) What is the mean number (±0.0001) of students in your sample who do not say that they stole something from a store in the past year?

=

(c) What is the standard deviation (±0.0001) of the number of students in your sample who say that they stole something?

=

(d) Suppose that you live in a city where only 5% of the high school students say that they stole something from a store in the past year.

What is (±0.0001) in this case?

=

Explanation / Answer

Solution:

Using binomial distribution with parameter

p = 10% = 0.10

number of trials n=10

(a) mean = np=10*0.10 = 1

(b) here P(students say that they donot stole something from a store in the past year)=1-p=1-0.10=0.90

in this case mean = n(1-p)=10*0.90 = 9

(c) standard deviation = sqrt(n*p*(1-p))=sqrt(10*0.10*0.90)=sqrt(0.9)=0.94868

(d) here p=0.05 and n=12 then standard deviation = sqrt(n*p*(1-p))=sqrt(10*0.05*0.95)=0.68920

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