SOLUTION: 5) The weight of a newborn is a random variable X which has the standard normal distribution with the mean weight is 3 kg. The standard deviation  = 0.2 kg. The minimum wei

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Question 388626: 5) The weight of a newborn is a random variable X which has the standard normal distribution with the mean weight is 3 kg. The standard deviation  = 0.2 kg. The minimum weight of newborn is 1.5 kg.
a) Calculate the probability of newborn that has the weight within the interval 3kg to 3.4kg.
b) The newborn that has the weight less than 2.5kg is deprived of weight. Calculate the probability of newborn that deprived of weight.
c) The newborns in 10% of the smallest weight need look after careful. Calculate the maximum weight of newborn that need look after careful.
Found 2 solutions by stanbon, unknown000:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The weight of a newborn is a random variable X which has the standard normal distribution with the mean weight is 3 kg. The standard deviation  = 0.2 kg. The minimum weight of newborn is 1.5 kg.
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a) Calculate the probability of newborn that has the weight within the interval 3kg to 3.4kg.
z(3 kg) 0
z(3.4 kb) = (3.4-3)/1.5 = 0.4/1.5 = 0.267
P(3< x < 3.4) = P(0< z < 0.267) = 0.1052
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b) The newborn that has the weight less than 2.5kg is deprived of weight. Calculate the probability of newborn that deprived of weight.
z(1.5) = (1.5-3)/1.5 = -1
z(2.5) = (2.5-3)/1.5 = -0.5/(1.5) = -1/3
P(1.5 < x < 2.5) = P(-1< z <-1/3) = 0.2108
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c) The newborns in 10% of the smallest weight need look after careful. Calculate the maximum weight of newborn that need look after careful.
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Find the z-value interval that has that 10% of the population.
Area below x = 1.5 = Area below z=-1 is 0.1587
The next 10% interval includes a left-tail of 0.2587
The z-value for that left tail is -0.6475
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Max weight in that interval is : x = zs+u
x = -0.6475*1.5+3 = 2.0290 kg
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Cheers,
Stan H.

Answer by unknown000(1) About Me  (Show Source):
You can put this solution on YOUR website!
why divide by minimum weight=1.5, do not divide by standard derivation 0.2
thanks