Answer to Question #106508 in Statistics and Probability for Palesa

Question

The mean weight of adult women is 69:4 kg with standard deviation of 8:9 kg.a) Which normal distribution can be taken as a model for the population distribution of the variable weight of an adult woman?b) Calculate the probability that the weight of 1 randomly chosen woman is at most 70 kg.c)let X be the mean weight of 10 random women,Determine the probability distribution of X.d) Calculate the probability that this sample mean is at most 70 kg.e)Calculate the probability that the sample mean is between 65kg and 75kg.

Answer 1

a) N ~ (69.4, 79.21)

b) $P(X<70)=P(Z<\frac{70-69.4}{8.9})=P(Z<0.07)=0.5279.$

c) N~ (69.4, 7.921)

d) $P(X<70)=P(Z<\frac{70-69.4}{\frac{8.9}{\sqrt{10}}}=P(Z<0.21)=0.5832.$

e) $P(65<X<75)=P(\frac{65-69.4}{\frac{8.9}{\sqrt{10}}}<Z<\frac{75-69.4}{\frac{8.9}{\sqrt{10}}})=$

$=P(-1.56<Z<1.99)=P(Z<1.99)-P(Z<-1.56)=0.9173.$