Math Is Fun Forum

Calculate the surface integral:
∫ ∫ with s on bottom. F dot dS where F (x,y,z) = = (2x + y + z ; x + 2y + z ; x + y + 2z)
where S is the surface of the box bounded by the planes x = 0, x = 1, y = 0, y = 4, z = 0, z = 5

I used the divergence theorem and got 120.

1   What is the probability that an outcome z is less than -0.5?

0.3085

2   What is the probability that an outcome z is between -1 and 1.5?

0.7745

3   What would be the 91th percentile (P91) for such a N(0,1) distribution?

1.34

4   For a certain population diastolic blood pressure has been evaluated to have a mean value
of 75, a 10th percentile (P10) of 55, an 80th percentile (P80) of 90, and a range of 60. What
can we say for sure about diastolic blood pressure in that population?

Third quartile can't be more than 90.

According to a recent article in the journal "Appetite," 70% of 2 to 5 year old children
living in the US suffer from food neophobia. We choose at random five 2 to 5 year old
children living in the US.

5   What is the probability that at least four of the chosen children suffer from food
neophobia?

0.528

6   What is the probability that the number of children suffering from food neophobia
among the five chosen is between one and three, both inclusive?

0.6

According to a recent article in the journal "Environmental Health Perspectives," the
amount of soil ingested in one day by infants living in a particular town is a random
variable with a normal distribution with mean 20 g and variance 4. Assume that is
really the case.

7   What is the probability that an infant chosen at random from that town will ingest
more than 25 grams of soil in one day?

0.8944

8   What is the probability that an infant chosen at random from that town will ingest
less than 15 grams of soil in one day?

0.9876

9   Now assume that we chose at random 4 infants from that town. What is the
probability that none of them will ingest more than 25 grams of soil in one day?

0.9754

10   Suppose we flip a fair coin 10 times. What is the probability that we will get heads
every single time? 0.001

11   Now suppose we flip a coin that has heads on both sides. What is now the
probability that we will get heads every single time?   1, obviously.

A clinic has four departments, headed by doctor A, doctor B, doctor C, and doctor D,
respectively. Dr. A's department is treating 10 patients at this time, Dr. B's department is
treating 2 patients, Dr. C's department is treating 5 patients, and Dr. D's department is
treating 4 patients.
A patient from the clinic is chosen to be entered in a new clinical trial after informed
consent. The procedure to choose such a patient is the following: first a department in
the clinic is chosen at random, and then a patient from the chosen department is chosen
also at random.

12   What is the probability that John R, a patient treated by Dr. C, will be chosen to
enter the clinical trial?  0.05

13   What is the probability that Mary H., a patient in Dr. A's department, will be
chosen to enter the clinical trial?

0.025

One or two might be wrong so I need someone to check them. Reviewing for the final exam (our prof. gave me many pages like this). Thank-you in advance.