Statistics and Probability Answers

12 students are to pose for photographs after a social gathering at FCT. 4 students are from Lagos state, 3 are from Kano state and the remaining are from Kwara state. How many possible photographs can they take if students from the same state must stand close to one another?

12 jobseekers applied for 3 available vacant positions in a company. In how many ways can the job be offered among these applicants if a particular applicant must be employed?

2. Suppose that the average outstanding credit card balance for young professionals is

Php11,200 with standard deviation of Php 2,600. In simple random sample of 150 young

professionals, what is the probability that the mean outstanding credit card balance does

not exceeds Php12,300?

(HINT: Central Limit Theorem)

10. The length of time, in minutes, for an airplane to wait for clearance to take off at a certain

airport is a random variable Y = 3X − 2, where X has the density function

f(x) = {1/4^e−x/4, 0.

x > 0

elsewhere,

Find the mean and variance of the random variable Y.

9. The probability density function for a diameter of a drilled hole in millimeters is f(x) =

10e^−10(x−5)

for x > 5 mm. Although the target diameter is 5 mm, vibrations, tool wear,

and other nuisances produce diameters larger than 5 mm.

a) Determine the mean and variance of the diameter of the holes. [Hint: Use

integration by parts.]

b) Determine the probability that the hole exceeds 5.1 mm.

8. Suppose the probability density function of the length of computer cables is f(x) = 0.1

from 1200 to 1210 millimeters.

a) Determine the mean and standard deviation of the cable length.

b) If the length specifications are 1195 < x < 1205, what proportions of cables are

within specifications?

The density function of the thickness of a conducive coating in micrometers is f(x) =

600x^−2

for 100 < x < 120.

a) Determine the mean and variance of the coating thickness.

b) If the coating costs $0.50 per micrometer of thickness on each part, what is the

average cost of the coating per part?

Suppose that contamination particle size (in micrometers) can be modeled as f(x) =

2x^−3

for x > 1. Determine the mean and standard deviation of X.

5. The maximum patent life for a new drug is 17 years. Subtracting the length of time

required by the FDA for testing and approval of the drug provides the actual patent life

of the drug – that is, the length of time that a company has to recover research and

development costs and make profit. Suppose the distribution of the lengths of patent life

for new drugs is as shown here:

x 3 4 5 6 7 8 9 10 11 12 13

f(x) 0.03 0.05 0.07 0.10 0.14 0.20 0.18 0.12 0.07 0.03 0.01

a) Find the expected number of years of patent life for a new drug.

b) Find the standard deviation of x.

c) Find the probability that x falls into the interval μ ± 2σ.

4. You can insure a $50,000 diamond for its total value by paying a premium of D dollars. If

the probability of theft in a given year is estimated to be 0.01, what premium should the

insurance company charge if it wants the expected gain to equal $1000?