According to a survey, 26 % of residents of a country 25 years old or older had earned at least a bachelor's degree. You are performing a study and would like at least 10 people in the study to have earned at least a bachelor's degree. (a) How many residents of the country 25 years old or older do you expect to randomly select? (b) How many residents of the country 25 years old or older do you have to randomly select to have a probability 0.985 that the sample contains at least 10 who have earned at least a bachelor's degree?

Question

Mathematics

Dakota Rich

2 June, 07:16

According to a survey, 26 % of residents of a country 25 years old or older had earned at least a bachelor's degree. You are performing a study and would like at least 10 people in the study to have earned at least a bachelor's degree. (a) How many residents of the country 25 years old or older do you expect to randomly select? (b) How many residents of the country 25 years old or older do you have to randomly select to have a probability 0.985 that the sample contains at least 10 who have earned at least a bachelor's degree?

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Answers (1)

Know the Answer?

Kenzie · Answer 1

a) 39

b) 64

Step-by-step explanation:

a) in order to know how many residents of the country that are 25 years old or older do you expect to randomly select? we say;

Let the number of residents be x

0.26*x >=10

x > = 10/0.26 = 38.46

~ 39

b) in order to know How many residents of the country 25 years old or older do you have to randomly select to have a probability 0.985 that the sample contains at least 10 who have earned at least a bachelor's degree we say;

P (at least 10 out of 9) = 1-P (at most 9) = 0.983

solving above : number of randomly selected residents = 64