Statistics and Probability Answers

In 2015, the mean return of all common stocks on the Philippine Stock Exchange was 3.5%. The standard deviation of the returns was about 26%. A student of finance forms all possible portfolios that invested equal amounts in 5 of these stocks and records the return for each portfolio. This return is the average of the returns of the 5 stocks chosen. What are the mean and standard deviation of the portfolio returns?

A molding machine prepares a certain kind of car spare part with a target diameter μ = 40.265 millimeters. The machine has some variability so the standard deviation of the diameters is σ = 0.004 millimeters. A sample of 6 spare parts is inspected each hour for process control purposes and records are kept of the sample mean diameter. What will be the mean and standard deviation of the numbers recorded?

the scores of individual students on a national test have a normal distribution with mean of 18.6 and standard deviation of 5.9. At Federico Ramos Rural High School, 76 students took the test. If the scores at this school have the same distribution as national scores, what are the mean and standard deviation of the sample mean for 76 students?

Consider a population consisting of 1,2,3,4 and 5. Supposed samples of size 2 are drawn from this population. describe the sampling distribution of the sample means.

• What is the mean and variance of the sampling distribution of the sample means?
• Compare these values to the mean and variance of the population.
• Draw the histogram of the sampling distribution of the population mean.

Mean and Variance of the Probability Distribution

Find the mean and the variance of the following probability distribution.

X P(X)

1 0.237

2 0.317

3 0.178

4 0.157

5 0.070

The following are data obtained from rolling a die several times. Compute the mean and variance of the frequency distribution.

Outcome Number of Occurrences

1 4

2 8

3 6

4 12

5 3

6 7

1. The height of grade 1 pupils is are approximately normally distributed with µ = 45 inches and σ
2. σ
3. σ
4. σ
5.  = 6.
6. If an individual pupil is selected at random, what is the probability that he or she has a height of 42 and 47?
7. A class of 30 of these pupils is used as a sample. What is the probability that the class mean is between 42 and 47?
8. If a pupil is selected at random, what is the probability that is taller than 46 inches?
9. A class of 30 of these pupils is used as sample. What is the probability that the class mean is greater than 46 inches?

 The time taken to complete a particular type of a job is distributed approximately normally with mean 1.8 and standard deviation of 0.1hours.

Given that ‘’normal-time’’ work ends at 6pm and a job is started at 4.00pm, determine the probability that the job will need overtime.                         (2marks)

Calculate the estimated completion time (to the nearest minute) that should be set so that there is a 90% chance that the job is completed on time.                 (3marks)

A recent survey showed that 60 percent of the population own some kind of microcomputer and 40 percent do not. Market experts predict that in a year 10 percent of the non owners will become owners, and 1/100 of one percent of the owners will become nonowners.

a) What are the transition matrix of owners and nonowners for next year?

b) What is the predicted steady state for the next year?

A restaurant chain regularly surveys its customers. On the basis of these surveys, the management of the chain claims that 75% of its customers rate the food as excellent. A consumer testing service wants to examine the claim by asking 460 customers to rate the food.

Seventy per cent rated the food as excellent. Does this support the management’s claim?