Recent research suggests that Americans make an average of 1

Recent research suggests that Americans make an average of 10 phone calls per day (CNN, August 26, 2010). Let the number of calls be normally distributed with a standard deviation of 3 calls. Use Table 1.

a.
What is the probability that an average American makes between 4 and 12 calls per day? (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)

Probability

b.
What is the probability that an average American makes more than 6 calls per day? (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)

Probability

c.
What is the probability that an average American makes more than 16 calls per day? (Round \"z\" value to 2 decimal places and final answer to 4 decimal places.)

Probability

Solution

Normal Distribution
Mean ( u ) =10
Standard Deviation ( sd )=3
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 4) = (4-10)/3
= -6/3 = -2
= P ( Z <-2) From Standard Normal Table
= 0.02275
P(X < 12) = (12-10)/3
= 2/3 = 0.6667
= P ( Z <0.6667) From Standard Normal Table
= 0.74751
P(4 < X < 12) = 0.74751-0.02275 = 0.7248                  
b)
P(X > 6) = (6-10)/3
= -4/3 = -1.3333
= P ( Z >-1.333) From Standard Normal Table
= 0.9088                  
c)
P(X > 16) = (16-10)/3
= 6/3 = 2
= P ( Z >2) From Standard Normal Table
= 0.0228