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2 years ago

Express 75000000000 in scientific and calculator notation

Mathematics

2 answers:

anygoal [31]2 years ago

8 0

$7.5*10^{10}$ in scientific notation (also called standard form).

Butoxors [25]2 years ago

7 0

The scientific notation:

$a\cdot10^k\\\\1\leq a < 10,\ k\in\mathbb{Z}$

$7\underbrace{5,000,000,000.}_{\leftarrow10}=7.50000000000\cdot10^{10}=7.5\cdot10^{10}$

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Answer:

a) 0.4770

b) 3.9945

c) z-statistics seem a large value

Step-by-step explanation:

a. Find the standard deviation of the sample proportion based on the null hypothesis

Based on the null hypothesis:

$p_{0}$ : 0.35

and the standard deviation σ = $\sqrt{p_{0} *(1-p_{0}) }$ = $\sqrt{0.35 *0.65 }$ ≈0.4770

b. Find the z statistic

z-statistic is calculated as follows:

z= $\frac{X-p_{o} }{\frac{s}{\sqrt{N} } }$ where

X is the proportion of employees in the survey who take advantage of the Credit Union ( $\frac{138}{300}=0.46$ )
$p_{0}$ is the proportion in null hypothesis (0.35)
s is the standard deviation (0.4770)
N is the sample size (300)

putting the numbers in the formula:

z= $\frac{0.46-0.35} }{\frac{0.4770}{\sqrt{300} } }$ = 3.9945

c. Does the z statistic seem like a particularly large or small value?

z-statistics seem a large value, which will cause us to reject the null hypothesis.

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