A survey of adults found that 34% say their favorite sport is professional footb

Question

A survey of adults found that 34% say their favorite sport is professional football. You randomly select 160 adults and ask them if their favorite sport is professional football. (a) Find probability that at most 77 people say their favorite sport is professional football. (b) Find the probability that more than 41 people say their favorite sport is professional football. (c) Find the probabilities that between 52 and 63 people, inclusive, say their favorite sport is professional football. (d) Are any of the probabilities in parts (a)-(c) unusual? Explain. Use a normal approximation to the binomial distribution if possible. (a) The probability that at most 77 people say their favorite sport is professional football is (Round no four decimal places as needed.)

Explanation / Answer

Ans:a) sample proportion=77/160=0.48

Population proportion=0.34

z=(0.48-0.34)/sqrt(0.34*(1-0.34)/160)=0.14/0.0374

z=3.743

P(z<3.743)=0.9999

b)sample proportion=41/160=0.26

z=(0.26-0.34)/sqrt(0.34*(1-0.34)/160)=-0.08/0.0374=-2.14

P(z>-2.14)=1-0.01618=0.98382

c) for 52, sample proportion=52/160=0.325

for 63, sample proportion=63/160=0.394

z=(0.325-0.34)/0.0374=-0.401

z=(0.394-0.34)/0.0374=1.444

P(-0.401<z<1.444)=P(z<1.444)-P(z<-0.401)=0.92563-0.34421=0.58142

d) all probabilities are greater than 0.05,hence all are usual.

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