Download Q1 - JustAnswer

Q1. A normal population has a mean of 20.0 and a standard deviation of 4.0.
a. What proportion of the population is between 20.0 and 25.0?
b. What proportion of eh population is less than 18.0?
25  20
 1.25
4.0
a.
1.25 found by z 
b.
0.3944, found in Appendix D
c.
0.3085, found by z 
18  20
 0.5
2.5
Find 0.1915 in Normal Distribution table for z = – 0.5 then 0.5000 – 0.1915 = 0.3085
Q2. The number of viewers of American Idol has a mean of 29 million with a standard
deviation of 5 million. Assume the is distribution follows a normal distribution. What is
the probability that next week's show will:
a. Have between 30 and 40 million viewers?
b. Have at least 23 million viewers?
c. Exceed 40 million viewers.
Let X be the number of viewers of American Idol. Given that X is normal with mean µ =
29 million and standard deviation  = 5 million.
Standardizing the variable X using Z 
X 


X  29
and from standard normal tables,
5
we can find the probabilities as follows.
What is the probability that next week's show will have between 30 and 34 million
viewers?
 30  29 X   34  29 


P (30 < X < 34) = P 

5 
 5
= P (0.2 < Z < 1)
= 0.262
Distribution Plot
Normal, Mean=0, StDev=1
0.4
0.262
Density
0.3
0.2
0.1
0.0
0 0.2
X
1
What is the probability that next week's show will have at least 23 million viewers?
We need P (X ≥ 23).
 X   23  29 

P (X ≥ 23) = P 
= P (Z ≥ -1.2) = 0.8849
5 
 
Distribution Plot
Normal, Mean=0, StDev=1
0.4
0.3
Density
0.8849
0.2
0.1
0.0
-1.2
0
X
What is the probability that next week's show will exceed 40 million viewers?
We need P (X > 40).
 X   40  29 

P (X > 40) = P 
= P (Z > 2.2) = 0.0139
5 
 
Distribution Plot
Normal, Mean=0, StDev=1
0.4
Density
0.3
0.2
0.1
0.0
0.0139
0
X
2.2