Mathematics & Economics Math Problem: Mathematics assignment

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Question 1: (3 marks)
In the most recent election, 20%of all eligible college students voted. If a random sample of10 students were surveyed,
* Find the probability that exactly half of them voted in the election? 
P (V) = 20% =0.2
P (voted), 10 students = 20%*10= 2 students
P( 10 students half voted)= 2* 0.5 =1 student
P( half voted)= 0.2*0.5=0.1
* Find the probability that none of them voted in the election? 
P (V) = 20% =0.2
P (Vc) = 100%-20% =0.8
* Find the probability that at least one of them voted in the election? 
P (V∩Vc) =0.2*0.8= 0.16
Question 2: (2 marks)
At an ocean side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water that is discharged back into the ocean. The amount that the water temperature is raised has a uniform distribution over the interval from 10° to 25° C.
* What is the probability that the temperature increase will be less than 20° C? 
Z = (X - μ) / σ
Mean (μ) = (10° C+ 25° C)/ 2=17.5 ° C
Standard deviation (σ) = 10.6066
Z = (20-17.5/ 10.61) = 0.2357
P(X < 20) =0.41
* What is the probability that the temperature increase will be between 20° C and300 C?
Z = (X - μ) / σ
Z = (30-17.5/ 10.61) = 1.1785
P= .119299
P (20
Question 3: (3 marks)
Suppose that the times required for a cable company to fix cable problems in its customers' homes are normally distributed with mean 45 minutes and standard deviation 15 minutes.
* What is the probability that a randomly selected cable repair visit will take at least 36 minutes? 
Z = (X - μ) / σZ = (36 - 45) / 15Z = -0.6
The P-Value is .274253
P(X > 36) ≈ 1 − .2742≈ 0.7257
* What is the probability that a randomly selected cable repair visit will take at most 60 minutes? 
Z = (X - μ) / σZ = (60 - 45) / 15Z = 1