According to a survey, 27% of residents of a country 25 years old or order had e

Question

According to a survey, 27% of residents of a country 25 years old or order had earned at least a bachelor's degree. You are performing a study and wood the at least 10 people in the study to have earned at least a bachelor's degree. When technology is used, use the Tech Help button for further assistance. (a) How many residents of the country 25 years old or order 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 0.984 that the sample contains at least 10 who have earned at least a bachelor's degree? (a) The number of randomly selected residents is. (b) The number of randomly selected resident with a probability 0.984 containing at least 10 who have earned at least a bachelor's degree is .

Explanation / Answer

according to question, there is survey where 27% of people older than 25 years of age are graduate. I have to find atleast 10 people who have earned a bachelor's degree.

(a) lets say i have selected X people for survey, i would to expect to get X * 0.27 people graduate, so to get atleast 10 people, the survey should be of

0.27 X = 10

X = 37.03 or say 37 persons

(b) Here we have to calculate the sample size. Here the probability to find atleast 10 people graduate is 0.984 Let say there are X member in sample size

so expected graduates in the sample = 0.27X

and the value of standerd deviation = sqrt( 0.27 * X * 0.73) = 0.4440 (X)

so Here P( x>= 10; 0.27 X, 0.4440X) = 0.984

so  P( x <= 10; 0.27 X, 0.4440X) = 1- 0.984 = 0.016

so Z value related to that probability is -2.145

so for the negative z - value = (X - mean)/ standerd deviation

- 2.145 = ( 10 - 0.27 X) /00.4440X

0.9523 X = 0.27X - 10

0.9069 X = (0.27X - 10) 2 = 0.0729 X2 + 100 - 5.4 X

0.0729 X2 - 6.307 X + 100 = 0

X = [6.307 + sqrt ( 39.777 - 29.16)] / 2 * 0.0729 = 65.60 or 66 people must be studied

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