Suppose we have a binomial experiment in which success is defined to be a partic

Question

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us (a) Suppose n-45 and p 0.27. Can we approximate p by a normal distribution? Why? (Use 2 decimal places.) nq = Yes Can be approximated by a normal random variable because both np and nq exceed What are the values of up and op? (Use 3 decimal places.) op (b) Suppose n 25 and p = 0.15. Can we safely approximate p by a normal distribution? why or why not? | , p cannot be approximated by a normal random variable because np does not exceed 0 (c) Suppose n = 49 and p = 0.25. Can we approximate p by a normal distribution? why? (Use 2 decimal places.) np = nq = Yes r P Can be approximated by a normal random variable because both np and nq exceed What are the values ofMp and Og? (Use 3 decimal places.) op

Explanation / Answer

Solution:-
a) n = 45 , p = 0.27 , q = 1-p = 0.73

np = 45*0.27 = 12.15
nq = 45*0.73 = 32.85

=> mean = np = 12.150
  
sd = sqrt(npq) = sqrt(45*0.27*0.73) = 2.978

b) n = 49 , p = 0.25 q = 1-0.25 = 0.75

np = 49*0.25 = 12.25
nq = 49*0.75 = 36.75

=> mean = np = 12.250
  
sd = sqrt(npq) = sqrt(49*0.25*0.75) = 3.031

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