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
![P(|\overline X-\mu|\le0.5) = P\left(\left|\dfrac{\overline X-\mu}{0.25}\right|\le\dfrac{0.5}{0.25}\right) = P(|Z|\le 2) \approx \boxed{0.95}](https://tex.z-dn.net/?f=P%28%7C%5Coverline%20X-%5Cmu%7C%5Cle0.5%29%20%3D%20P%5Cleft%28%5Cleft%7C%5Cdfrac%7B%5Coverline%20X-%5Cmu%7D%7B0.25%7D%5Cright%7C%5Cle%5Cdfrac%7B0.5%7D%7B0.25%7D%5Cright%29%20%3D%20P%28%7CZ%7C%5Cle%202%29%20%5Capprox%20%5Cboxed%7B0.95%7D)
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
![P(|\overline X-\mu| < 0.4) = 0.95](https://tex.z-dn.net/?f=P%28%7C%5Coverline%20X-%5Cmu%7C%20%3C%200.4%29%20%3D%200.95)
Comparing to the equation from the previous part, this means we would need
![\dfrac{0.4}{\frac{2.5}{\sqrt{n}}} = 0.16\sqrt n = 2 \implies \sqrt n = 12.5 \implies n = 156.25](https://tex.z-dn.net/?f=%5Cdfrac%7B0.4%7D%7B%5Cfrac%7B2.5%7D%7B%5Csqrt%7Bn%7D%7D%7D%20%3D%200.16%5Csqrt%20n%20%3D%202%20%5Cimplies%20%5Csqrt%20n%20%3D%2012.5%20%5Cimplies%20n%20%3D%20156.25)
so a sample of at least 157 men would be sufficient.
Answer:
B) 36
Step-by-step explanation:
If x = 10, then evaluating the value of 6(x - 4) involves using the distributive property of multiplication, which will allow us to further simplify an expression by taking out the parentheses.
Substitute the value of x into the algebraic expression:
6(10 - 4)
Next, subtract the integers inside the parenthesis, then distribute the 6 from outside the parenthesis:
6(6) = 36.
Therefore, the correct answer is B: 36.
Area of a Triangle = A = ½ (b × h) square units
Step-by-step explanation:
where B and C are the base and height of the triangle, respectively.
10) The GCF of a set of numbers is the largest number that divides into both numbers.
The GCF of 24 and 36 is 12.
15)
can be simplified by dividing the top (numerator) and the bottom (denominator) by the GCF. The GCF of 30 and 54 is 6. The new fraction is
. 6/9
20) The GCF of
is 11. The new fraction is
. 5/8
Answer:
8x - 4
Step-by-step explanation:
8x - 4