Question

The book club of the month has determined that a quarter of its members purchase the line offered as a monthly selection. if a random sample of 300 members is selected, what is the probability that:

a) more than 0.18 of the members will buy the selected book

b) less than 0.28 of the members will buy the selected book

c) within which limits of the population proportion will be found 99% of the sample proportions

d) if the club has a total of 1200 members, what would be the answer of subsection a?

P(ps>=0.19)

Answer 1

The book club of the month has determined that a quarter of its members purchase the line offered as a monthly selection. if a random sample of 300 members is selected, what is the probability that:

p=0.25

Standard deviation of p = sqrt(0.25*(1-0.25)/300)) =0.025

a) more than 0.18 of the members will buy the selected book

z value for 0.18, z =(0.18-0.25)/0.025 = -2.8

P(ps >0.18) = P(z > -2.8) =0.9974

b) less than 0.28 of the members will buy the selected book

z value for 0.28, z =(0.28-0.25)/0.025 =1.2

P(ps <0.28) = P(z < 1.2) =0.8849

c) within which limits of the population proportion will be found 99% of the sample proportions

z value for 99% = 2.576

lower bound = 0.25-2.576*0.025 =0.1856

upper bound = 0.25+2.576*0.025 = 0.3144

d) if the club has a total of 1200 members, what would be the answer of subsection a?

1200*0.9974 =1196.88

Answer: 1197 members.

P(ps>=0.19)

z value for 0.19, z =(0.19-0.25)/0.025 =-2.4

P(ps >0.19) = P(z > -2.4) =0.9918