Please help, due soon. show work for the problem

A scientist claims that 7% 7 % of viruses are airborne. If the scientist is accurate, what is the probability that the proportio

Reptile [31]

Answer:

The probability is $P(|p-\^{p}| > 0.03) = 0.0040$

Step-by-step explanation:

From the question we are told that

The population proportion is $p = 0.07$

The mean of the sampling distribution is $\mu_p = 0.07$

The sample size is n = 600

Generally the standard deviation is mathematically represented as

$\sigma_p = \sqrt{\frac{p (1 -p)}{n} }$

=> $\sigma_p = \sqrt{\frac{0.07(1 -0.07)}{600} }$

=> $\sigma_p = 0.010416$

Generally the probability that the proportion of airborne viruses in a sample of 600 viruses would differ from the population proportion by greater than 3% is mathematically represented as

$P(|p-\^{p}| > 0.03) = 1 - P(|p -\^{p}| \le 0.03)$

=> $P(|p-\^{p}| > 0.03) = 1 - P(-0.03 \le p -\^{p} \le 0.03 )$

Now add p to both side of the inequality

=> $P(|p-\^{p}| > 0.03) = 1 - P( 0.07-0.03 \le \^{p} \le 0.03+ 0.07 )$

=> $P(|p-\^{p}| > 0.03) = 1 - P(0.04 \le \^{p} \le 0.10 )$

Now converting the probabilities to their respective standardized score

=> $P(|p-\^{p}| > 0.03) = 1 - P(\frac{0.04 - 0.07}{0.010416} \le Z \le \frac{0.10 -0.07}{0.010416} )$

=> $P(|p-\^{p}| > 0.03) = 1 - P(-2.88 \le Z \le 2.88 )$

=> $P(|p-\^{p}| > 0.03) = 1 - [P(Z \le 2.88) - P(Z \le -2.88)]$

From the z-table

$P(Z \le 2.88) = 0.9980$

and

$P(Z \le -2.88) = 0.0020$

So

$P(|p-\^{p}| > 0.03) = 1 - [0.9980 - 0.0020]$

=> $P(|p-\^{p}| > 0.03) = 0.0040$

7 0

3 years ago

Never really understood this stuff. can somebody help me out? Please and thank you. (two different questions)

kodGreya [7K]

The answer to the first question is 138.125 because you would multiply all those numbers together to get volume

8 0

2 years ago

Read 2 more answers

You are biking to the park. After six minutes 40% of the distance still need to be traveled. How long does it take to bike to th

nikklg [1K]

Answer:

$y = (100-10x)\%$

It takes <em>10 minutes</em> to the park.

Step-by-step explanation:

Given that:

Time taken = 6 minutes

Distance left to be traveled = 40%

To find:

The equation to represent the distance $y$ , that still needs to be traveled after $x$ minutes.

Solution:

As per given statement, distance traveled in 6 minutes = 60%

We can say that:

Distance traveled each minute = $\frac{60\%}{6}$ = 10%

After 1 minute, distance traveled = 10%

Distance left = 100 - 10 = 90%

After 2 minutes, distance traveled = 20%

Distance left = 100 - 20 = 80%

After $x$ minutes, distance traveled = 10 $x$ %

Distance left, $y$ = (100 - 10 $x$ )%

Therefore, the equation is:

$y = (100-10x)\%$

Time taken by the bike to reach to the park can be found by putting $y$ = 0 (i.e. distance left to be traveled = 0)

$0 = 100 -10x\\\Rightarrow 10x = 100\\\Rightarrow x = \bold{10\ minutes}$

8 0

3 years ago

A picture is 5 cm longer than it is wide. the perimeter of the picture is 90cm. What is the width of the picture?

Igoryamba

Perimeter=2L+2W
L=W+5, substitute in place of 2L
90=2(W+5)+2W
90=2W+10+2W
90-10=4W
80=4W
80/4=W
W=20, if width is 20 than the length is 20+5=25 cm

8 0

3 years ago

Ollie earns a fixed amount of $2,700 per month and a commission of 12% on all of his sales for the month. To cover all of his ex

mrs_skeptik [129]

Answer:

The amount of sales in order to cover his monthly expenses must be greater than or equal to $22,500

Step-by-step explanation:

Let

x----> represent the amount of sales Ollie will need

we know that

The amount of sales for the month multiplied by the commission rate as a decimal plus the fixed amount must be greater than or equal to $5,400 each month

so

The inequality that represent this situation is

$0.12x+2,700\geq 5,400$