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The standard deviation of heights for students in a school is 0.81. A random sample of 50 students is taken, and the standard deviation of heights of the sample is 0.96. A researcher in charge of the study believes the standard deviation of heights for the school is greater than 0.81.

a) State the null and alternative hypotheses.

b) State the degree of freedom.

c) What can you conclude at the 5% significance level?


A random sample of 30 pair of observations from a normal population gives a correlation coefficient of 0.32 . Is it likely that the variable in the coefficient are correlated?

Find an equation of the sphere that has center (2,3,-1) and contains the point (1,7,-9)


Find an equation of the sphere that has radius 1 and center in the first octant and is tangent to each coordinate plane


Find an equation of the sphere that has endpoints of a diameter at A and B


A(1,4,-2) B(-7,1,2)


Find an equation of the sphere with center c that is tangent to (a) the xy-plane, (b) the xz- plane and (c) the yz-plane


(i)C(-2,4,-6)


Find an equation of the sphere with center c that is tangent to (a) the xy-plane, (b) the xz- plane and (c) the yz-plane


(i)C(-2,4,-6)


(x^2D^2-xD+1)y=sin (logx)

Find the vector that has (a) the same direction as A and twice the magnitude of A, (b) the opposite direction of a and one-third the magnitude of a, and (c) the same direction as A and magnitude 2.


(i)A=14i-15j+6k


L + x be a nœemal randome variable with mean 4 and variouse dot alpha Find the probability 8li * e_{s}


1) Between 4 and 6


2) Between 5 and 7.5


3) ・2 and 3.


4) greater them d * 75


5) Less than 4.025.


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