Answer to Question #292025 in Statistics and Probability for loop

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

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