Question

The Pew Internet and American Life Project reported in 2004 that “17% of current music down loaders say they are using paid services”. Consider a random sample of 400 music down loaders. Compute the probability that X equals the mean of X where X is the number of current music down loaders (You can use appropriate program). Find the mean of X. Find the probability?

Answer 1

Solution:

Given that,

p = 17% = 0.17

n = 400

Here, BIN (400 , 0.17)

Mean = E(X) = n * p = 400 * 0.17 = 68

we can use normal approximation to binomial to find P(X = 68)

According to normal approximation binomial,

X Normal

Mean = = n*p = 400 * 0.17 = 68

Standard deviation = =   =   = 7.5126559884

Now ,

P(X = Mean)

= P(X = 68)

= P[68 - 0.5 < X < 68 + 0.5]

= P[67.5 < X < 68.5]

= P(X < 68.5) - P(X < 67.5 )

=  P[(X - )/ <  (68.5- 68 )/7.5126559884] -   P[(X - )/ <  (67.5 - 68 )/7.5126559884]

= P[Z < 0.0666] - P[Z < -0.0666]

= 0.5265 - 0.4735 ..Use z table

= 0.0530