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P(x=0)(4 0)(0.1667)(1 - 0.1667)^4 = 0.4822 ...both bad eggs end up in the breakfast? P(x = z)=(4 2)(0.1667^2)(1-0.1667)^2=0.1158 it is estimated that the balance on credit cards issued by Frost Bank have a Normal distribution with a mean of $845 and a standard deviation of $270. For a randomly selected balance, what is the probability that... ...it is between $1100 and 1440 ...is is at least $750? ...it is less than $1600?

Solution

Normal Distribution
Mean ( u ) =845
Standard Deviation ( sd )=270
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 1100) = (1100-845)/270
= 255/270 = 0.9444
= P ( Z <0.9444) From Standard Normal Table
= 0.82753
P(X < 1440) = (1440-845)/270
= 595/270 = 2.2037
= P ( Z <2.2037) From Standard Normal Table
= 0.98623
P(1100 < X < 1440) = 0.98623-0.82753 = 0.1587                  
b)
P(X < 750) = (750-845)/270
= -95/270= -0.3519
= P ( Z <-0.3519) From Standard Normal Table
= 0.3625                  
P(X > = 750) = 1 - P(X < 750)
= 1 - 0.0393 = 0.9607                  
c)
P(X < 1600) = (1600-845)/270
= 755/270= 2.7963
= P ( Z <2.7963) From Standard Normal Table
= 0.9974