Question 388626
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.