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 = 39 and p = 0.18. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.) np = nq = , p̂ be approximated by a normal random variable because . What are the values of μp̂ and σp̂? (Use 3 decimal places.) μp̂ = σp̂ = (b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not? , p̂ be approximated by a normal random variable because . (c) Suppose n = 61 and p = 0.26. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.) np = nq = , p̂ be approximated by a normal random variable because . What are the values of μp̂ and σp̂? (Use 3 decimal places.) μp̂ = σp̂ =

Answer 1

a)

np=	7.02
n(1-p)=	31.98

p̂ be approximated by a normal random variable because np and nq >=5

here population proportion=     μp=

0.180

std error of proportion=σp=√(p*(1-p)/n)=

0.062

b)

np=	3.75
n(1-p)=	21.25

p̂ cannot be approximated by a normal random variable because np <5

c)

np=	15.86
n(1-p)=	45.14

p̂ be approximated by a normal random variable because np and nq >=5

here population proportion=     μp=

0.260

std error of proportion=σp=√(p*(1-p)/n)=

0.056