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notka56 [123]
3 years ago
11

In the United States, the mean and standard deviation of adult men's heights are 70 inches (5 feet 10 inches) and 4 inches, resp

ectively. Suppose the American adult men's heights have a normal distribution Whe probability that a randomly chosen American man is taller than 6 feet (72 inches) is equal to:___________. (round off to fourth decimal place, use the given table)
a. 0.6853
b. 0.0062
c. 0.3085
d.0.6915
e. None of these
Mathematics
1 answer:
Artyom0805 [142]3 years ago
5 0

Answer:

P(X>72)=P(\frac{X-\mu}{\sigma}>\frac{72-\mu}{\sigma})=P(Z>\frac{72-70}{4})=P(z>0.5)

And we can find this probability using the complement rule and the normal standard table:

P(z>0.5)=1-P(z

And the best solution would be:

c. 0.3085

Step-by-step explanation:

For this case we can convert all the values to inches in order to standardize the solution:

5ft * \frac{12 in}{1ft}= 60 in

6ft * \frac{12 in}{1ft}= 72 in

Let X the random variable that represent the heights of US mens, and for this case we know the distribution for X is given by:

X \sim N(70,4)  

Where \mu=70 and \sigma=4

We are interested on this probability

P(X>72)

We can use the z score formula given by:

z=\frac{x-\mu}{\sigma}

Using this formula we got:

P(X>72)=P(\frac{X-\mu}{\sigma}>\frac{72-\mu}{\sigma})=P(Z>\frac{72-70}{4})=P(z>0.5)

And we can find this probability using the complement rule and the normal standard table:

P(z>0.5)=1-P(z

And the best solution would be:

c. 0.3085

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3 years ago
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Answer:

\large \boxed{\$4100.07}

Step-by-step explanation:

The formula for the future value (FV) of an investment earning compound interest is

FV = PV \left (1 + \frac{r}{n} \right )^{nt}

where

PV = the present value (PV) of the money invested

  r = the annual interest rate expressed as a decimal fraction

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Data:

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Calculation:

\begin{array}{rcl}\\7100& =& PV \left (1 + \dfrac{0.08}{2} \right )^{2 \times 7}\\\\& =& PV (1 + 0.04)^{14}\\\\& =&PV (1.04)^{14}\\& =& PV(1.731676)\\PV& =& \dfrac{7100}{1.731676}\\\\& =& \mathbf{4100.07}\\\end{array}\\\text{The present value of the money is $\large \boxed{\mathbf{\$4100.07}}$}

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Answer:

-37

Step-by-step explanation:

-16+-11=-27

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