Fill in the blank: 1) In a normal distribution, the empirical rule states approx

Question

Fill in the blank: 1) In a normal distribution, the empirical rule states approximately 95% of the observed data fall within standard deviation of the mean. 2) In a normal distribution, the empirical rule states approximately 99.7% of the observed data fall within standard deviation of the mean. 3) Given two independent random variables with Eleft(x_1 ight)=mu_1,Varleft(x_1 ight)=sigma^2_1,Eleft(x_2 ight)=mu_2,Varleft(x_2 ight)=sigma^2_2E(x1)=1,Var(x1)=12,E(x2)=2,Var(x2)=22; If we transform the data using the linear combination y=3x_1-5x_2y=3x15x2, then Eleft(y ight)=E(y)= , Varleft(y ight)=Var(y)= (write answers in terms of E(X1), E(X2), Var(X1), Var(X2) respectively) (for the following use P(A) and P(B) in your answers * can be used for multiplication, NULL for null set) 4) Given A and B are mutually exclusive then Acap B=AB= 5) Given A and B are independent then Pleft(Acap B ight)=P(AB)= 6) Given A and B are independent then Pleft(Amid B ight)=P(AB)= 7) Given A and B are dependent then Pleft(Acap B ight)=P(AB)= 8) Given n(E)=21 and P(E)=0.7, then O(E)= 9) Data is skewed to the left when the mean is to the of the median. 10) The probability of the sample space is . 11) The probability of any event is between and . 12) Given P(E)=0.62, then Pleft(E^c ight)=P(Ec)= 13) Let n(E) be the number of outcomes in an event E. Given n(E)=21 and P(E)=0.6, then nleft(E^c ight)=n(Ec)=

Explanation / Answer

Fill in the blank: 1) In a normal distribution, the empirical rule states approximately 95% of the observed data fall within 2 standard deviation of the mean.

2) In a normal distribution, the empirical rule states approximately 99.7% of the observed data fall within

3 standard deviation of the mean.

for the other question please post it in a new question

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