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erma4kov [3.2K]
2 years ago
5

A Pharmacist whishes to mix a solution that is 6% Minoxidil. She has on hand 100 ml of 4% solution and wishes to add some 8% sol

ution to obtain the desired 6% solution. How much 8% solution should she add?
Mathematics
1 answer:
Kaylis [27]2 years ago
8 0

Answer:

She would need 100 ml of the 8% solution

Step-by-step explanation:

You can always answer these questions using a proportion. The numerator will represent the amount of Minoxidil, and the denominator will represent the total amount of solution

She already ha 100 ml of a 4% solution. That means that she has 4 ml of Minoxidil already

\frac{4 + 0.08(S)}{100 + S} =\frac{6}{100}

We can multiply both sides by 100 for simplicity

\frac{400 + 8S}{100+S}=6\\ 400 + 8S =6(100 + S)\\400 + 8S = 600 + 6S\\2S = 200\\S = 100

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Suppose the test scores for a college entrance exam are normally distributed with a mean of 450 and a s. d. of 100. a. What is t
svet-max [94.6K]

Answer:

a) 68.26% probability that a student scores between 350 and 550

b) A score of 638(or higher).

c) The 60th percentile of test scores is 475.3.

d) The middle 30% of the test scores is between 411.5 and 488.5.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 450, \sigma = 100

a. What is the probability that a student scores between 350 and 550?

This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So

X = 550

Z = \frac{X - \mu}{\sigma}

Z = \frac{550 - 450}{100}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 350

Z = \frac{X - \mu}{\sigma}

Z = \frac{350 - 450}{100}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a student scores between 350 and 550

b. If the upper 3% scholarship, what score must a student receive to get a scholarship?

100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88

Z = \frac{X - \mu}{\sigma}

1.88 = \frac{X - 450}{100}

X - 450 = 1.88*100

X = 638

A score of 638(or higher).

c. Find the 60th percentile of the test scores.

X when Z has a pvalue of 0.60. So it is X when Z = 0.253

Z = \frac{X - \mu}{\sigma}

0.253 = \frac{X - 450}{100}

X - 450 = 0.253*100

X = 475.3

The 60th percentile of test scores is 475.3.

d. Find the middle 30% of the test scores.

50 - (30/2) = 35th percentile

50 + (30/2) = 65th percentile.

35th percentile:

X when Z has a pvalue of 0.35. So X when Z = -0.385.

Z = \frac{X - \mu}{\sigma}

-0.385 = \frac{X - 450}{100}

X - 450 = -0.385*100

X = 411.5

65th percentile:

X when Z has a pvalue of 0.35. So X when Z = 0.385.

Z = \frac{X - \mu}{\sigma}

0.385 = \frac{X - 450}{100}

X - 450 = 0.385*100

X = 488.5

The middle 30% of the test scores is between 411.5 and 488.5.

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