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7.43: Let denote the random variable for height and
for the sample mean. Then if
is the mean of
So the probability that the difference between the sample and population means does not exceed 0.5 inch is
per the empirical or 68/95/99.7 rule.
7.44: For a sample of size <em>n</em>, the sample standard deviation would be . We want to find <em>n</em> such that
Comparing to the equation from the previous part, this means we would need
so a sample of at least 157 men would be sufficient.
Answer:
- geometric sequence with initial value 20 and common ratio 1/2
- average rate of change on [1, 3] = -7.5
Step-by-step explanation:
(a) The given points have sequential values of x and values of y that are each 1/2 the value before. The common ratio tells us the sequence is a geometric sequence.
(b) The first given point is (2, 10), so extrapolating backward, we determine the previous point to be ...
... (2-1, 10/(1/2)) = (1, 20)
Thus, we have enough information to determine the average slope between n=1 and n=3.
... (difference in y)/(difference in n) = (5 -20)/(3 -1) = -15/2 = -7.5
