According to Nielsen Media Research, 25% of T-s are tuned to NFL Monday Night Fo

Question

According to Nielsen Media Research, 25% of T-s are tuned to NFL Monday Night Football when it is televise Assuming the show is being broadcast and that 30 TV-s are randomly selected: 1. Determine the mean, variance, and standard deviation for the distribution 2. Determine the probability that 5 [out of 30 TV-s] are tuned to NFL Monday Night Football 3. Less than 10 [out of 30 TV-s] are tuned to NFL Monday Night Football 5. Find the most expected number of TV-s [out of 30 TV-s], that are tuned to NFL Monday Night Footbal

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 51
standard Deviation ( sd )= 3
a.
P(X < 43) = (43-51)/3
= -8/3= -2.6667
= P ( Z <-2.6667) From Standard Normal Table
= 0.0038
b.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 48) = (48-51)/3
= -3/3 = -1
= P ( Z <-1) From Standard Normal Table
= 0.1587
P(X < 52) = (52-51)/3
= 1/3 = 0.3333
= P ( Z <0.3333) From Standard Normal Table
= 0.6306
P(48 < X < 52) = 0.6306-0.1587 = 0.4719
c.
P ( Z < x ) = 0.8413
Value of z to the cumulative probability of 0.8413 from normal table is 0.999815
P( x-u/s.d < x - 51/3 ) = 0.8413
That is, ( x - 51/3 ) = 0.999815
--> x = 0.999815 * 3 + 51 = 53.999445 ~ 54

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