Question

According to the National Restaurant Association, 23% of fine-dining restaurants have instituted policies restricting the use of cell phones. Do not use PHStat or Excel for this part. Compute the values manually.

a. If you select a sample of 125 fine-dining restaurants, what is the probability that the sample has between 18% to 28% restaurants that have established policies restricting the use of cell phones?

b. If you select a sample of 125 fine-dining restaurants, compute the symmetrical limits within which the sample percentage will be contained 95% of the time.

Answer 1

a)

for normal distribution z score =(p̂-p)/σp
here population proportion=     p=	0.230
sample size       =n=	125

  probability that the sample has between 18% to 28% restaurants that have established policies restricting the use of cell phones:

probability =

P(0.18<X<0.28)

=

P(-1.33<Z<1.33)=

0.9082-0.0918=

0.8164

b)

for middle 95% values; critical z =1.96

therefore:

symmetrical limits within which the sample percentage will be contained 95% of the time =0.23 -/+1.96*0.0376

=0.1562 to 0.3038 ~ 15.62% to 30.38%