Answer to Question #135377 in Statistics and Probability for Kistam Priyanka

Question #135377
Suppose height to the bottom of clouds is a gaussian random variable X for which mean ax = 4000 m, and standard deviation sx = 1000m. A person bets that cloud height tomorrow will fall in the set A={1000m < Xs 3300m) while a second person bets that height will be satisfied by B= (2000m < Xs 4200m). A third person bets they are both correct. Find the probabilities that each person will win the bet.
1
Expert's answer
2020-09-29T18:25:21-0400

XN(aX,sX2)X\sim N(a_X, s_X^2 )

Given aX=4000m,sX=1000ma_X=4000 m, s_X=1000m

A first person and a second person will be right when cloud height will fall in the set ABA\cap B ={2000m < X< 3300m)


P(2000<X<3300)=P(2000<X<3300)=

=P(Z<330040001000)P(Z200040001000)==P(Z<\dfrac{3300-4000}{1000})-P(Z\leq\dfrac{2000-4000}{1000})=

=P(Z<0.7)P(Z2)=P(Z<-0.7)-P(Z-\leq2)\approx

0.241963650.022750130.2192\approx0.24196365-0.02275013\approx0.2192

If A first person and a second person will be right then and a third person will be right

The probability that each person will win the bet is 0.21920.2192.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment