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ira [324]
3 years ago
7

The distribution of vitamin C amount in vitamin drops produced by a given factory is approximately Normal, with a mean of 60.0 m

g and a standard deviation of 0.5 mg.
About 80% of vitamin drops contain more than
A 59.36 mg of vitamin C.
B 59.58 mg of vitamin C.
C 60.42 mg of vitamin C.
D 60.64 mg of vitamin C.

Mathematics
2 answers:
bagirrra123 [75]3 years ago
5 0
<span>You have to calculate z-scores for each of these values and then compare them with what is needed for the 80%tile on a Normal curve.
 
z = (value - mean)/(standard deviation) = (value-60.0)/0.5.
z= 1 has 84% of the values smaller.</span>
PIT_PIT [208]3 years ago
4 0

Answer:

The correct answer is option (B) 59.58 mg of vitamin C.

Step-by-step explanation:

See the attached file for the calculation

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A museum conducts a survey of its visitors in order to assess the popularity of a device which
Natali5045456 [20]

Answer:

i:

The appropriate null hypothesis is H_0: p \geq 0.2

The appropriate alternative hypothesis is H_1: p < 0.2

The p-value of the test is 0.1057 > 0.05, which means that there is not sufficient evidence that fewer than 20% of the museum visitors make use of the device, and so, it should not be withdrawn.

ii:

The p-value of the test is 0.1057

Step-by-step explanation:

Question i:

The device will be withdrawn if fewer than 20% of all of the museum’s visitors make use of it.

At the null hypothesis, we test if the proportion is of at least 20%, that is:

H_0: p \geq 0.2

At the alternative hypothesis, we test if the proportion is less than 20%, that is:

H_1: p < 0.2

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

0.2 is tested at the null hypothesis:

This means that \mu = 0.2, \sigma = \sqrt{0.2*0.8} = \sqrt{0.16} = 0.4.

The device will be withdrawn if fewer than 20% of all of the museum’s visitors make use of it. Of a random sample of 100 visitors, 15 chose to use the device.

This means that n = 100, X = \frac{15}{100} = 0.15

Test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.15 - 0.20}{\frac{0.4}{\sqrt{100}}}

z = -1.25

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion below 0.15, which is the p-value of z = -1.25.

Looking at the z-table, z = -1.25 has a p-value of 0.1057.

The p-value of the test is 0.1057 > 0.05, which means that there is not sufficient evidence that fewer than 20% of the museum visitors make use of the device, and so, it should not be withdrawn.

Question ii:

The p-value of the test is 0.1057

7 0
2 years ago
57=100<br> 36=?%<br><br> 36=?%.............
ivolga24 [154]

Answer:

?= 63.15789474%

Step-by-step explanation:

Use cross multiply

Set ?=x

57 \times x = 100 \times 36 \\ 57x = 3600 \\  \frac{57x}{57}  =  \frac{3600}{57}  \\ x =  \frac{3600}{57} \\ x = 63.15789474

8 0
2 years ago
Read 2 more answers
Please help me with my math I’m so bad at this
mojhsa [17]

Answer:

9

Step-by-step explanation:

(-9)^1/3 * (-81)^1/3

We can rewrite -81 as 9 * -9

So it can be rewritten as:

(-9)^1/3 * (9*-9)^1/3

Since they are all raised to the 1/3, we can combine the bases:

(-9*9*-9)^1/3 =

(9*9*9)^1/3, because the two negatives turn into a positive:

So this is basically:

(9^3)^1/3 = 9^1 = 9

7 0
2 years ago
Answer the question in the picture above.
Anvisha [2.4K]

Answer:

m is less than A apparently

Step-by-step explanation:

3 0
2 years ago
When number can each term of the equation be multiplied by to eliminate the fractions before solving 6-3/4x+1/3=1/2x+5​
PolarNik [594]

Answer:

12

Step-by-step explanation:

You need to find the least common denominator (LCD) to all the denominators of the fractions present in the equation. These denominators are (writing them in their prime factor form to make our calculations easier):

4=2^2\\3=3\\2=2

Therefore, we need to include a factor of 3, and two factors of 2 (2^2) in our least common denominator, so this LCD will be a perfectly divided by all three given denominators, therefore eliminating all fractions in the equation.

Our LCD is = 3*2^2=13*4=12

6 0
2 years ago
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