Question

A random sample of size n = 40 is selected from a binomial distribution with population proportion p = 0.25.

Describe the approximate shape of the sampling distribution of p̂.

approximately normalskewed left    uniformskewed right

Calculate the mean and standard deviation (or standard error) of the sampling distribution of p̂. (Round your standard deviation to four decimal places.)

mean standard deviation

Find the probability that the sample proportion p̂ is between 0.15 and 0.41. (Round your answer to four decimal places.)

Answer 1

since

np=	10
n(1-p)=	30

both are greater than 5;

approximately normal

2)

mean μp=0.25

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

0.0685

3)

probability =P(0.15<X<0.41)=P((0.15-0.25)/0.068)<Z<(0.41-0.25)/0.068)=P(-1.46<Z<2.34)=0.9904-0.0721=0.9183