Question

A local florist claims that 85% of all flowers sold for Valentine’s Day are roses. Consider a
simple random sample of 150 orders for Valentine’s Day flowers.
(a) What’s the probability that the proportion of roses in this sample is more than
90%? Round your answer to four (4) decimal places.
(b) What’s the probability that the proportion of roses in this sample is at most
78%? Round your answer to four (4) decimal places.
(c) What’s the probability that the proportion of roses in this sample differs from
the population proportion by more than 15%? Round your answer to four (4) decimal
places.

Answer 1

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.8500
sample size       =n=	150
std error of proportion=σp=√(p*(1-p)/n)=	0.0292

a)

probability =P(X>0.9)=P(Z>(0.9-0.85)/0.029)=P(Z>1.71)=1-P(Z<1.71)=1-0.9564=0.0436

b)

probability =P(X<0.78)=(Z<(0.78-0.85)/0.029)=P(Z<-2.401)=0.0082

c)

probability =1-P(0.7<X<1)=1-P((0.7-0.85)/0.029)<Z<(1-0.85)/0.029)=1-P(-5.14<Z<5.14)=1-1=0.0000