Question

It has been reported that 78% of adults between the ages of 30 and 49 years use Facebook. If we survey a simple random sample of n = 520 adults between the ages of 30 and 49 years and ask if they use Facebook, the percentage who say “yes” will vary if the sampling method is repeated. In fact, the sampling distribution of the percentage of adults between the ages of 30 and 49 years who say they use Facebook in many samples of size n = 520, will be Normal in shape, with mean (or center) of 78% (or 0.78) and standard deviation of 1.8% (or 0.018). Based on this information, we know that the probability of obtaining a sample of size n = 520 adults between the ages of 30 and 49 years where 75% or fewer say they use Facebook is

A. 0.0227. B. 0.0359. C. 0.0446. D. 0.0500. E. 0.1357.

Answer 1

P(< 0.75)

= P(( - )/< (0.75 - )/)

= P(Z < (0.75 - 0.78)/0.018)

= P(Z < -1.67)

= 0.0475

Option - D) 0.0500