Suppose FOX claims that commercial breaks are 200 seconds lo

Suppose FOX claims that commercial breaks are 200 seconds long with a standard deviation of 24 secones. If you measure the length of 49 commericals,

1) what is the P [the average of these commercials is between 194 and 206 seconds]?

2) what is the P [the average of these commercials is more than 210 seconds]?

Solution

Normal Distribution
Mean ( u ) =200
Standard Deviation ( sd )=24
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 194) = (194-200)/24
= -6/24 = -0.25
= P ( Z <-0.25) From Standard Normal Table
= 0.40129
P(X < 206) = (206-200)/24
= 6/24 = 0.25
= P ( Z <0.25) From Standard Normal Table
= 0.59871
P(194 < X < 206) = 0.59871-0.40129 = 0.1974                  

b)
P(X > 210) = (210-200)/24
= 10/24 = 0.4167
= P ( Z >0.417) From Standard Normal Table
= 0.3385