Q. NO1

MATHEMATICAL EXPECTATION/

DISCRETE PROBABILITY DISTRIBUTIONS

A)The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. What is the expected number of admissions for the fall semester? Compute the variance and the standard deviation of the number of admissions.

Admissions 1000 1200 1500

Probability 0.6 0.3 0.1

B)The probability that a patient recovers from a rare blood disease is 0.4. If 15 people are known to have contracted this disease, what is the probability that

(a)at least 10 survive, (b) from 3 to 8 survive, and (c) exactly 5 survive?

C)Lots of 40 components each are deemed unacceptable if they contain 3 or more defectives. The procedure for sampling a lot is to select 5 components at random and to reject the lot if a defective is found. What is the probability that exactly 1 defective is found in the sample if there are 3 defectives in the entire lot?

D)Ten is the average number of oil tankers arriving each day at a certain port. The facilities at the port can handle at most 15 tankers per day. What is the probability that on a given day tankers have to be turned away?

Q. NO2

NORMALDISTRIBUTION/ SAMPLING DISTRIBUTION

A)A certain machine makes electrical resistors having a mean resistance of 40 ohms and a standard deviation of 2 ohms. Assuming that the resistance follows a normal distribution and can be measured to any degree of accuracy, what percentage of resistors will have a resistance exceeding 43 ohms?

B)Tartus Industries has seven production employees (considered the population). The hourly earnings of each employee are given in the following table.

Employee Joe Sue Sam Jon Bob Art Ted

Earning($) 14 14 16 16 14 16 18

i)What is the population mean?

ii)What is the sampling distribution of the sample mean for samples of size 2?

iii)What is the mean of the sampling distribution?

iv)What observations can be made about the population and the sampling

distribution?

Q. NO3

CONFIDENCE INTERVAL FOR ONE POPULATION MEAN

A)A researcher wishes to estimate the number of days it takes an automobile dealer to sell a Chevrolet Aveo. A random sample of 50 cars had a mean time on the dealer's lot of 54 days. Assume the population standard deviation to be 6.0 days. Find the best point estimate of the population mean and the 95% confidence interval of the population mean.

B)The archaeologist discovered only nine fossil skeletons of an unknown species of miniature horse. Reconstructions of the skeletons of these miniature horses show the following shoulder heights;

45.347.144.2 46.846.545.5 47.6 45.7 46.4

(a) Estimate the Sample Mean and Sample Standard Deviation.

(b) Using student's t-distribution table, estimate the error E at 95% confidence.

(c) Estimate the interval of population mean having 95% confidence level.

Q. NO4

HYPOTHESIS TESTING FOR ONE POPULATION MEAN

A)Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna). A random sample of nine of these birds was caught, weighed, and released in a remote part of the Grand Canyon. The weights observed (in grams) were :

3.72.9 3.8 4.2 4.8 3.1 3.5 4.3 3.0

Let x be a random variable representing weights of Anna's hummingbirds in this part of the Grand Canyon. Assuming x has a normal distribution with sample standard deviation 0.648. The population mean is 4.55 grams.

(a) Calculate the Sample Mean of the above mentioned data values.

(b) Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.55 grams? Establish the Null and Alternate Hypothesis.

(c) Compute the Test statistics of the sample data using Student's t-distribution table. Take = 0.05

(d) Find the P-value or range of P-values.

(e) Conclude the test and interpret the result.

B)A researcher believes that the mean age of medical doctors in a large hospital system is older than the average age of doctors in the United States, which is 46. Assume the population standard deviation is 4.2 years. A random sample of 30 doctors from the system is selected, and the mean age of the sample is 48.6. Test the claim at = 0.05.