Question

# The extract of a plant native to Taiwan has been tested as a possible treatment for...

The extract of a plant native to Taiwan has been tested as a possible 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 77 and a standard deviation of 5.5 grams per milliliter.

(a)  What is the probability that the amount of collagen is greater than 67 grams per milliliter?

(b)  What is the probability that the amount of collagen is less than 90 grams per milliliter?

(c)  What percentage of compounds formed from the extract of this plant fall within 3 standard deviations of the mean?

Solution :

Given that ,

mean = = 77

standard deviation = = 5.5

a) P(x > 67) = 1 - p( x< 67)

=1- p P[(x - ) / < (67 - 77) / 5.5]

=1- P(z < -1.82)

Using z table,

= 1 - 0.0344

= 0.9656

b) P(x < 90)

= P[(x - ) / < (90 - 77) / 5.5]

= P(z < 2.36)

Using z table,

= 0.9909

c) 77  ± 3 * 5.5 = 60.5, 93.5

P(60.5 < x < 93.5) = P[(60.5 - 77)/ 5.5) < (x - ) /  < (93.5 - 77) / 5.5) ]

= P(-3.0 < z < 3.0)

= P(z < 3.0) - P(z < -3.0)

Using z table,

=0.9987 - 0.0013

= 0.9974

The percentage is = 99.74%

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