It is known that the birth weight of newborn babies in Austr

It is known that the birth weight of newborn babies in Australia has a mean of 4 kilograms with a standard deviation of 1.1 kilograms. Suppose we randomly select 64 babies and record the birth weight, what is the probability the average birth weight will be less than 3.75 kilograms?

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0.0754

0.0345

0.0246

0.9655

The distribution of the time that a battery pack for a laptop computer can function before requiring recharging is normal with a mean of 6 hours and standard deviation of 1.8 hours. 25 laptops with this type of battery pack are selected at random and tested. What is the probability that the average time until recharging is necessary is at least 7 hours?

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0.0027

0.9973

0.0017

0.9965

Solution

Q1.
Mean ( u ) =4
Standard Deviation ( sd )=1.1
Number ( n ) = 64
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 3.75) = (3.75-4)/1.1/ Sqrt ( 64 )
= -0.25/0.1375= -1.8182
= P ( Z <-1.8182) From Standard NOrmal Table
= 0.0345                  

Q2.
Mean ( u ) =6
Standard Deviation ( sd )=1.8
Number ( n ) = 25
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X < 7) = (7-6)/1.8/ Sqrt ( 25 )
= 1/0.36= 2.7778
= P ( Z <2.7778) From Standard NOrmal Table
= 0.9973                  
P(X > = 7) = 1 - P(X < 7)
= 1 - 0.9973 = 0.0027