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et X and Y be continuous random variables having joint density functio
The following sample data are from a normal population: 10, 8, 12, 16, 13, 11, 6, 4. a. What is the point estimate of the population mean? 10 b. What is the point estimate of the population standard deviation (to 2 decimals)? 15.13 c. With 95% confidence, what is the margin of error for the estimation of the population mean (to 1 decimal)? 3.8 d. What is the 95% confidence interval for the population mean (to 1 decimal)?
Assume that random guesses are made for eight multiple choice questions on an SAT test, so that there are n=8 trials, each with probability of success (correct) given by p=0.2. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 4.
The “Titans” cricket team has a winning rate of 75%. The team is planning to play 10 matches in the next season.
a) Let X be the number of matches that will be won by the team. What are the possible values of X?
b) What is the probability that the team will win exactly 6 matches?
c) What is the probability that the team will lose 2 or less matches?
d) What is the mean number of matches that the team will win?
e) What are the variance and the standard deviation of the number of matches that the team will win?
Low-cost airlines are more likely to have delays than premium airlines.
regulations dictate that for any production process involving COVID 19 vaccine,
the water in the output of the process must not exceed 7950 parts per million (ppm)
of COVID 19 vaccine. For a particular process of concern, the water sample was
collected by a manufacturer ‘55’ times randomly and the sample average was 7960
ppm. It is known from historical data that the standard deviation σ is 100 ppm.
What is the probability that the sample average in this experiment would exceed the
government limit if the population mean is equal to the limit? Use the Central Limit
Theorem.
of aspirin per tablet, with a standard deviation of 55/10 mg. Find the 95% tolerance
limits that will contain 90% of the tablet contents for this brand of buffered aspirin.
Assume that the aspirin content is normally distributed.
x= 1, 2, 3, 4, 5, 6, 7, 8
f= 136, 60, 34, 12, 55, 1, 3, 1
Test the hypothesis, at the 0.05 level of significance, does the distribution of grades
follow poisson distribution.
regulations dictate that for any production process involving COVID 19 vaccine,
the water in the output of the process must not exceed 7950 parts per million (ppm)
of COVID 19 vaccine. For a particular process of concern, the water sample was
collected by a manufacturer ‘55’ times randomly and the sample average was 7960
ppm. It is known from historical data that the standard deviation σ is 100 ppm.
A firm buys 3 shipments of parts each month. The purchasing agent selects at random from among four in-state suppliers and six out-of-state suppliers. What is the probability that orders are placed with
a) The in-state suppliers only
b) The out-of-state suppliers only
c) At least one in- state suppliers
