Statistics and Probability Answers

In the 2019 midterm election, a pollster was assigned to interview the oldest male and female in various households. Each was asked whether he or she voted for Vico Sotto. If the male said “Yes” and the female said “No,” the pollster recorded YN. Construct the probability distribution of the number of YES answers then find the mean, variance, and standard deviation.​

The average number of milligrams (mg) of cholesterol in a cup of a certain brand of ice cream is 660 mg, and the standard deviation is 35 mg. Assume that the variable is normally distributed. If a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger than 670 mg?

1.     You are investing in two stocks: A and B, with normally distributed stock returns. Given the information on these two stocks, please use simulation to find the returns for A, B, and the portfolio for 20 years. Compute the theoretical and simulated mean and standard deviation of the portfolio return.

StockA

StockB

Mean

15%

8%

Sigma

30%

15%

Correlation

0.3

Proportion of A

60%

Summary of portfolio returns

Theoretical

Simulated

1.     You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two brands.

REQUIRED:

a)        What is the probability that the sample will have between 50% and 60% of the identifications correct?

Mrs. Santos wants to give her nephew two sweets from a jar she keeps on her kitchen table. There are 11 sweets in this jar.

7 of the sweets are red

4 of the sweets are orange

Calculate the probability that Mrs. Santos will take a sweet of each colour if she takes two sweets randomly from the jar.

Three Coins are tossed. Let T be the number of tails that occur.

a. Construct the probability Distribution for the random variable T.

b. Construct the probability histogram.

Consider all samples of size 5 from this population. 

1,3,5,9,11,12,15,26

1. Compute the mean and the standard deviation of the population. 

2. List all samples of size 5 and compute the mean for each sample. 

3. Construct the sampling distribution of the sample means.

4. Calculate the mean of the sampling distribution of the sample means. 

Compare this to mean of the population. 

5. Calculate the standard deviation of the sampling distribution of the 

sample means . Compare this to the standard deviation of the 

population. 

A sample size 40 from a non-normal population yielded the sample mean X= 71 and S² =200. Test H₀: µ=72 against H1: µ≠72. Use α= 0.05.

new machine is functioning well, 92% of the items produced are non- defective. Assume that a random sample of five parts produced on the machine is selected and we are interested in the number of defective parts found. Required: a) What are the conditions for this experiment to be considered a binomial experiment? Motivate. What is the probability that all parts selected will be defective? (3) c) What is the probability that none of the parts selected will be defective? (3) d) What is the probability that more than five parts will be defective? (2) e) What is the probability that at least three parts will be non-defective?

the cashier of a fastfood restaurant claims that the average amount spent by customers for dinner is P120. A sample of 50 customers over a month period was randomly selected and it was found out that the average amount spent for dinner was P122.50. Using a 0.05 level of significance, can it be concluded that the average amount spent by customer was more than P120? Assume that the population standard deviation is P6.50. (Use the low-value method)