Suzies heart was beating 90 beats a minute. How many minutes per beat is that?

A machine is used to fill Apple Juice bottles with juice. The machine has a known standard deviation of σ = 0.05 liters. The tar

Lina20 [59]

Answer:

The probability that the quality control manager will shut down the machine is 0.0002.

Step-by-step explanation:

We are given that a machine is used to fill Apple Juice bottles with juice. The machine has a known standard deviation of σ = 0.05 liters. The target mean fill volume is µ = 2.0 liters.

A quality control manager obtains a random sample of 50 bottles. He will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1.

Let $\bar X$ = sample mean fill volume

The z score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean fill volume = 2 liters

$\sigma$ = standard deviation = 0.05 liters

n = sample of bottles = 50

Now, it is provided that he will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1.

So, Probability that the sample of these 50 bottles is less than 1.95 is given by = P( $\bar X$ < 1.95)

P( $\bar X$ < 1.95) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{1.95-2}{\frac{0.05}{\sqrt{50} } }$ ) = P(Z < -7.07) = 1 - P(Z $\leq$ 7.07)

= 1 - 0.9999 = 0.0001

Probability that the sample of these 50 bottles is greater than 2.1 is given by = P( $\bar X$ > 2.1)

P( $\bar X$ > 2.1) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{2.1-2}{\frac{0.05}{\sqrt{50} } }$ ) = P(Z > 14.14) = 1 - P(Z < 14.14)

= 1 - 0.9999 = 0.0001

Because the highest critical value in the z table is given as x = 4.40 for area of 0.99999.

Therefore, probability that the quality control manager will shut down the machine = 2 $\times$ 0.0001 = 0.0002.

4 0

3 years ago

Find the sample size necessary in order to be 95% confident when determining the true mean weight within 2 units (EC2). Assume t

bogdanovich [222]

Answer:

(c) 43.

Step-by-step explanation:

Given:

Margin of error (E) = 2

Sample variance $(s^{2})$ = 44

Confidence level = 95%

The z- value at 95% confidence level is 1.96.

The sample using the provided information can be calculated as:

$n=(\frac{z(s)}{E})^{2} \\n=\frac{z^{2} s^{2} }{E^{2} } \\n=\frac{1.96^{2} (44) }{2^{2} }\\n= 42.52\\n=43$

Hence, the correct option is (c) 43.

8 0

3 years ago

Pls help me but pls dont send me a link im begging u

Vesna [10]

Answer:

Step-by-step explanation:

24 + 3r >= 100 is the equation

3 0

3 years ago

Read 2 more answers

If CDE ~ GDF, find ED

qaws [65]

Answer:

10

Step-by-step explanation:

$\triangle CDE \sim \triangle GDF.. (given) \\\\\therefore \frac{CD}{GD} =\frac{DE}{DF}.. (csst) \\\\\therefore \frac{15}{x+3} =\frac{3x+1}{4}\\\\ \therefore \: 15 \times 4 = (x + 3)(3x + 1) \\ \\ \therefore \: 60 = 3 {x}^{2} + x + 9x + 3 \\ \\ \therefore 3 {x}^{2} + 10x + 3 - 60 = 0 \\ \therefore 3 {x}^{2} + 10x - 57 = 0 \\ \therefore 3 {x}^{2} + 19x - 9x - 57 = 0 \\ \therefore \: x(3x + 19) - 3(3x + 19) = 0 \\\therefore \: (3x + 19)(x - 3) = 0 \\ \therefore \: 3x + 19 = 0 \: \: or \: \: x - 3 = 0 \\ \therefore \: x = - \frac{19}{3} \: \: or \: \: x = 3 \\ \because \: x \: can \: not \: be \: - ve \\ \therefore \: x = 3 \\ ED = 3x + 1 = 3 \times 3 + 1 \\ \huge \red{ \boxed{ ED= 10}}$

7 0

3 years ago

What is the surface area of a rectangular prism with a length of 3 mm, a width of 5 mm, and a height of 8 mm?

kherson [118]

158, because to solve this question we first need to know the formula for finding the surface area of a rectangular prism which is A=2(wl+hl+hw) then you just need to input the numbers like so A=2(5*3+8*3+8*5) then when you simplify this down you get A=2(79) then distribute like so so A=158

Enjoy!=)

8 0

3 years ago