With a height of 63 in, johnson was the shortest president of a particular club in the past century. the club presidents of the past century have a mean height of 66.5 in and a standard deviation of 1.3 in. a. what is the positive difference between johnson’s height and themean? b. how many standard deviations is that[the difference found in part(a)]? c. convert johnson’s height to a z score. d. if we consider "usual" heights to be those that convert to z scores between minus−2 and 2, is johnson’s height usual or unusual?

Step-by-step explanation:

Given that with a height of 63 in, Johnson was the shortest president of a particular club in the past century.

a) Positive difference between Johnson’s height and the mean=|63-66.5|=3.5 inches

b) No of std deviation the difference has =

c) Z score = no of std deviations from the mean = -2.692

d) Usual heights lie between -2 and 2.  Hence Johnson’s height is unusual

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.