Question

According to a article, 43% of all U.S. cellphone users are iPhone users. You believe this value is too low. You randomly select 100 of your peers that have cellphones and have determined that 52% of your sample are iPhone users. What is the probability of randomly selecting 100 cellphone users where the proportion who are iPhone users is more than 0.52?

a. What type of distribution are you using? Pick one of the following: “uniform distribution,”
“normal distribution,” “sampling distribution for x̅ ,” and “sampling distribution for p̂ .”

b. Is the distribution normal? How do you know?

c. What are the mean and standard deviation of your distribution?

d. Sketch a picture, shade, then find the probability of randomly selecting 100 cellphone
users where the proportion who are iPhone users is more than 0.52.

e. Look at your answer from part d. You collect another sample of 100 people and calculate
the proportion of them who are iPhone users, would you expect to get similar results to
what you saw (52% of your sample being iPhone users)?

Answer 1

a) sampling distribution for p̂ .

b) The exact distribution is not normal, we use Normal approximation to binomial since the sample size is large =100 and 100*0.43=43>10

100*(1-0.43)>10

e) 0.52 is sample proportion.This value does vary from sample to sample. It may so happen in next sample we get more I phone users taking the percentage higher or can get low I phone users taking the percentage lower.