Question

According to the article "Are Babies Normal?" by Traci Clemons and Marcello Pagano published in The American Statistician, Vol. 53, No. 4, pp. 298-302, the birth weights of babies are normally distributed with a mean of 3388 grams and a standard deviation of 595 grams.

1.What is the probability that a randomly selected baby weighs between 3000 grams and 3500 grams? Round your answer to 4 decimal places.

2.What is the probability that the average weight of 24 randomly selected 

Answer 1

1) $P(3000<X<3500)=P(\frac{3000-3388}{595}<Z<\frac{3500-3388}{595})=$

$=P(-0.65<Z<0.19)=P(Z<0.19)-P(Z<-0.65)=0.3175.$

2) $P(3000<\bar X<3500)=P(\frac{3000-3388}{\frac{595}{\sqrt{24}}}<Z<\frac{3500-3388}{\frac{595}{\sqrt{24}}})=$

$=P(-3.19<Z<0.92)=P(Z<0.92)-P(Z<-3.19)=0.8205.$