Answer:
The probability that fewer than 40 people from this sample access video-sharing sites is P=0.92.
Step-by-step explanation:
We have a populations proportion of internet users accessing video-sharing sites of p=0.71. We take a sample of n=50. This can be treated as a binomial random variable, but a normal distribution approximation is prefered, as the sample size is big to make all the calculations for the binomial distribution.
To approximate the binomial distribution to a normal distribution, we calculate the parameters as:
[tex]\mu=np=50*0.71=35.5\\\\\\\sigma=\sqrt{np(1-p)}=\sqrt{50*0.71*0.29}=3.2[/tex]
To calculate the probability that fewer that 40 people from this sample access video-sharing sites, we apply the continuity factor:
[tex]z=(X-\mu)/\sigma=(40-35.5)/3.2=4.5/3.2=1.406\\\\P_B(X<40)=P_N(X<39.5)=P(z<1.406)=0.92[/tex]
