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The following are the heights of students in centimeters suppose samples of size 2 are taken from this population of four students Cardo,Alyana, Joaquin, Flora heights; 125,120,130,110
A. Compute the mean of the population
B. Compute the mean of the sampling distribution of the sample means
: A computer program is tested by 3 independent tests. When there is an error, these tests will
discover it with probabilities 0.2, 0.3 and 0.5, respectively. Suppose that the program contains an
error. What is the probability that it will be found by at least one test.
A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability0.10 of giving a (false) positive when applied to a non- sufferer. It is estimated that 0.5 % of the population are sufferers. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this population). Calculate the following probabilities:
(a) that the test result will be positive.
(b) that, given a positive result, the person is a sufferer.
(c) that, given a negative result, the person is a non-sufferer.
The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered 1, 2,…, 6, then one outcome consists of computers 1 and 2, another consists of computers 1 and 3, and so on).
a. What is the probability that both selected setups are for laptop computers?
b. What is the probability that both selected setups are desktop machines?
c. What is the probability that at least one selected setup is for a desktop computer?
d. What is the probability that at least one computer of each type is chosen for setup?
a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit
can be used only once? (05)
(b) How many of these are odd numbers? (05)
(c) How many are greater than 330?
It is widely known that many drivers on interstate highways
in the United States do not observe the posted
speed limit. Assume that the actual rates of speed
driven by U.S. motorists are normally distributed with
mean mph and standard deviation 5 mph. Given this
information, answer each of the following independent
questions. (Hint: Use Goal Seek in parts a and b, and
use the Solver add-in with no objective in part c. Solver
is usually used to optimize, but it can also be used to
solve equations with multiple unknowns.)
a. If 40% of all U.S. drivers are observed traveling at
65 mph or more, what is the mean ?
b. If 25% of all U.S. drivers are observed traveling at
50 mph or less, what is the mean ?
c. Suppose now that the mean and standard deviation
of this distribution are both unknown. Furthermore, it
is observed that 40% of all U.S. drivers travel at less
than 55 mph and 10% of all U.S. drivers travel at more
than 70 mph. What must and be?
- The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight exceeds the maximum weight?
Aneco an Electrical Company claims that the average lifeof the bulbs it manufactures is 1,200 hours with a standard deviation of 250 hours. If random sample of 100 bulbs is chosen, what is the probability that the sample mean will be.
A sociologist believes that it costs more than P90,000 with a standard deviation of
P4,500 to raise a child from birth to age one. A random sample of 49 families, each with
a child is selected to see if this figure is correct. The average expenses for these families
reveal a mean of P92,000. Based on these sample data, can it be concluded that the
sociologist is correct in his claim? Use 0.05 level of significance.
Step:
1.State the null and alternative hypothesis
concerning the population mean, "\\mu" and the
type of test to be used
2. Specify the level of significance "\\alpha"
3. State the decision rule.
4. Collect the data and perform calculations.
5. Make a statistical decision.
6. State the conclusion.
What is the probability that a market inspector will discover, at least, two violations of the
public health code?
