11-7. Find the arithmetic mean, geometric mean and harmonic mean of the given
numbers.
(a) 1, 2 , 3 , 4 , 5 , 6 , 7 (b) 1 , 3 , 5 , 7 , 9 , 11 , 13 (c) 2 , 4 , 6 , 8 , 10 , 12 , 14
11-8. What is the probability of getting 10 consecutive heads in the toss of a fair
coin?
11-9. Given the following sample of ball bearing diameters, in inches, taken over
one production cycle.
Ball bearing diameters in inches
.738 .729 .743 .740 .736 .728 .735 .741 .737 .740
.735 .730 .736 .733 .745 .736 .742 .735 .734 .738
.734 .737 .732 .744 .741 .738 .732 .737 .742 .746
.739 .740 .735 .730 .744 .733 .727 .732 .734 .735
.724 .730 .739 .739 .733 .726 .735 .746 .731 .737
.738 .739 .735 .727 .735 .736 .744 .740 .736 .740
(a) Make a tally sheet and use the class marks {. 725 ,. 728 ,. 731 ,. 734 ,. 737 ,. 740 ,. 743 ,. 746 }
with class intervals of length ±. 0015 added to the class marks.
(b) Determine and sketch the frequency distribution and cumulative frequency dis-
tribution as well as the relative frequency distribution and cumulative relative
frequency distribution.
(c) Find the mean and variance directly.
(d) Find the mean and variance using the class marks and frequencies.
(e) Using the results from parts (a) and (b), approximate the following probabilities
if Xrepresents a random variable representing the diameter of a ball bearing.
(i)P(X≤.737) (ii)P(. 728 < X ≤.734) (iii)P(X > .734)
(f) In the absence of other information how can the relative frequency distribution
be interpreted?
11-10. A box contains 10 identical balls. Six of the balls are white and 4 of the
balls are black.
(a) What is the probability of drawing a white ball from the box?
(b) What is the probability of drawing a black ball from the box?
