Learn Decimals with Plainmath's In-Depth Explanations and Real-World Examples

Adult male height in America is normally distributed, with an average of 69.3 inches and a standard deviation of 2.67 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.54 inces. 
a) If a man is 6 feet 5 inches tall, what is z-score?

Test the claim that the proportion of people who own cats is significantly different than $50\mathrm{\%}$ at the 0.01 significance level. 
Based on a sample of 300 people, $41\mathrm{\%}$ owned cats 
Hint: Multiply to obtain the number of successes
$(\mathrm{\%}whoownedcats)(n)\to (41\mathrm{\%})(300)$ 
The test statistic is: ? (to 2 decimals) 
The p-value is: ? (to 4 decimals)

On average, there are 3 accidents per month at one intersection. We need to find out what is the probability that in any month at this intersection
a) What if there are 5 accidents?

b) What if there are less than 3 accidents?

c) What if there are at least 2 accidents?

Consider the quantity$a^2-b^2$ where a and b are real numbers.
(a) Under what conditions should one expect an unusually large relative error in the computed value of $a^2-b^2$ when this expression is evaluated in finite precision arithmetic?
(b)cWs 4-digit (decimal) rounding arithmetic to evaluate both $a^2-b^{2}and(a+b)(a-b)witha=995.1andb=995.0.$ Calculate th relative error in each result.
(c) The expression $(a+b)(a-b)isalgebraicallyequivalentto{a}^2-b^2,$ but it is a more accurate way to calculate this quantity if both a and b have exact floating point representations. Why?

Compute the following binomial probabilities directly from the formula for $b(x,n,p)$:

a) $b(3,8,0.6)$

b) $b(5,8,0.6)$

c) ${\displaystyle P(3\le X\le 5)}$

when $n=8$ and $p=0.6$

d)${\displaystyle P(1\le X)}$ when $n=12$ and $p=0.1$

Find the quadratic function that is best fit for f(x) defined by the table below

$\begin{array}{|cc|}\hline X& f(x)\\ 0& 0\\ 2& 401\\ 4& 1598\\ 6& 3595\\ 8& 6407\\ 10& 10,009\\ \hline\end{array}$