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 the probability that at most 78 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 probability that between 50 and 65 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 78 people say their favorite sport is professional football is Round to four decimal places as needed.) (b) The probability that more than 41 people say their favorite sport is professional football is (Round to four decimal places as needed.) (c) The probability that between 50 and 65 people, inclusive, say their favorite sport is professional football is Round to four decimal places as needed.) (d) Are any of the probabilities in parts (a)-(c) unusual? Explain. Select all that apply. A. Yes, the event in part (c) is unusual because its probability is less than 0.05 B. Yes, the event in part (b) is unusual because its probability is less than 0.0:5. C. Yes, the event in part (a) is unusual because its probability is less than 0.05. D. No, none of the probabilities is less than 0.05.

Explanation / Answer

here mean =np=160*0.34=54.4

and std deviaiton =sqrt(np(1-p))=5.992

a)

P(X<=78)=P(Z<(78.5-54.4)/5.992)=P(Z<4.02)=1.0000

b)

P(X>41)=P(Z>(41.5-54.4)/5.992)=P(Z>-2.15)=0.0158

( please try 0.0157 if above comes wrong due to rounding)

c)

P(50<=X<=65)=P(-0.82<Z<1.85)=0.9678-0.2061=0.7617

d)

option B

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