Question

It is known that 65 % of Facebook users are playing the free games (at least one) advertised by Facebook.
A) In a random sample of 315 Facebook users, what's the probability that less than 210 of them are playing the free games? (Round ˆp^, σˆp and your answer to 4 decimal places.)

B) In a random sample of 945 Facebook users, what's the probability that less than 630 of them are playing the free games? (Round ˆp^, σˆp and your answer to 4 decimal places.)

it is reported that 55 % of drivers are fueling their vehicle with Regular Unleaded Gasoline (Type 87 at any gas station).

A) In a random sample of 323 drivers filling their gas tanks at various stations, what's the probability that 190 to 210 of them are filling with Regular Unleaded Gasoline? (Round ˆpp^, σˆpσp^ and your answer to 4 decimal places.)

B) In a random sample of 969 drivers filling their gas tanks at various stations, what's the probability that 570 to 630 of them are filling with Regular Unleaded Gasoline? (Round ˆpp^, σˆpσp^ and your answer to 4 decimal places.)

It is known that 75 % of Asian population are infected with Hepatitis B.

A) In a random sample of 305 Asian patients, what's the probability that over 270 of them are infected with Hepatitis B? (Round ˆpp^, σˆpσp^ and your answer to 4 decimal places.)

B) In a random sample of 915 Asian patients, what's the probability that over 810 of them are infected with Hepatitis B? (Round ˆpp^, σˆpσp^ and your answer to 4 decimal places.)

Suppose a distribution has p=0.55p=0.55.

A) If a random sample of size N=19 is drawn, find μˆ_p, σˆ_p. (Round σˆpσp^ to four decimal places and the probability to four decimal places.)
μˆ_p= ?
σˆ_p=?

Answer 1

(A)

Here we have

p = 0.65, n=315

The sampling distribution of sample proportion of facebook users playing games will be approximately normal distribution with mean

and standard deviation

The z-score for   will be

The probability that less than 210 of them are playing the free games is

(B)

Here we have

p = 0.65, n=945

The sampling distribution of sample proportion of facebook users playing games will be approximately normal distribution with mean

and standard deviation

The z-score for   will be

The probability that less than 630 of them are playing the free games is