Jeff drinks 2/3 of a glass of juice. Write a fraction equivalent to 2/3

1 answer:

7 0

A fraction that means the same as 2/3 is 4/6.

To find this, you can simply multiple both the numerator and denominator (top and bottom) by any number as long as it's the same number for both top and bottom.
In this case, we used 2 as the number, and multipled it to the top and bottom of 2/3, to get 4/6.

I hope this helps!

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Answer:

a) 0.004

b) 0.9609

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 76503

Standard Deviation, σ = 8850

We are given that the distribution of annual salaries is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(salary greater than 100,000)

P(x > 100000)

$P( x > 100000) = P( z > \displaystyle\frac{100000 - 76503}{8850}) = P(z > 2.655)$

$= 1 - P(z \leq 2.655)$

Calculation the value from standard normal z table, we have,

$P(x > 100000) = 1 - 0.996 = 0.004 = 0.4\%$

b) P(sample mean annual salary falls between 70,000 and 80,000 dollars)

Sample size, n = 20

Standard error due to sampling =

$\dfrac{\sigma}{\sqrt{n}} = \dfrac{8850}{\sqrt{20}} = 1978.92$

$P(70000 \leq x \leq 80000) = P(\displaystyle\frac{70000 - 76503}{1978.92} \leq z \leq \displaystyle\frac{80000-76503}{1978.92})\\\\ = P(-3.286 \leq z \leq 1.767)\\\\= P(z \leq 1.767) - P(z < -3.286)\\=0.9614 - 0.0005= 0.9609 = 96.09\%$