The extract of a plant native to Taiwan has been tested as a pos- sible treatmen
ID: 3132417 • Letter: T
Question
The extract of a plant native to Taiwan has been tested as a pos- sible treatment for Leukemia. One of the chemical compounds produced from the plant was analyzed for a particular collagen. The collagen amount was found to be normally distributed with a mean of 65 and standard deviation of 9.3 grams per mililiter.
(a) What is the probability that the amount of collagen is greater than 62 grams per mililiter?
answer:
(b) What is the probability that the amount of collagen is less than 72 grams per mililiter?
answer:
(c) What percentage of compounds formed from the extract of this plant fall within 3 standard deviations of the mean?
answer: %
Thank you.
Explanation / Answer
A)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 62
u = mean = 65
s = standard deviation = 9.3
Thus,
z = (x - u) / s = -0.322580645
Thus, using a table/technology, the right tailed area of this is
P(z > -0.322580645 ) = 0.626493573 [ANSWER]
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b)
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 72
u = mean = 65
s = standard deviation = 9.3
Thus,
z = (x - u) / s = 0.752688172
Thus, using a table/technology, the left tailed area of this is
P(z < 0.752688172 ) = 0.77418134 [ANSWER]
************************
c)
This means a z score for -3 to 3.
z1 = lower z score = -3
z2 = upper z score = 3
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.001349898
P(z < z2) = 0.998650102
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.997300204 = 99.73% [ANSWER]
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