Statistics and Probability Answers

Solve the problem below.

Consider all samples of size of 5 from this population:

2, 5, 7, 9, 10, 11, 12

a. Compute the population mean.

b. Compute the population variance.

c. Compute the population standard deviation.

d. Compute the mean of the sampling distribution of the sample means and

compare it the mean of the population.

e. Compute the variance of the sampling distribution of the sample means.

f. Compute the standard deviation of the sampling distribution of the sample

means.

Compute for the mean of the set of numbers below. Write your answer on the

space provided in each item. Round off your answers to two decimal places.

1) 2, 5, 7, 3, 9

2) 12, 15, 7, 9, 10, 17

3) 3, 5, 7, 15, 17, 19, 21

4) 20, 32, 26, 22, 27, 30, 28, 21

5) 30, 35, 29, 34, 37, 40, 43, 36, 38

The COVID-19 pandemic and its containment measures have led to involuntary job loss and massive reduction in economic activities. Survey data if a small local community named Julau shows that 28 out of 60 individuals are currently unemployed due to the pandemic outbreak. As part of the initiatives to boost economic recovery, the government has rolled out an economic stimulus package called Prihatin National Aid- a one-off cash assistance for households and individuals in the lower income groups. Suppose that 15 individuals of the Julau community are randomly selected to received the Prihatin National Aid package. 

1. What is the probability that 9 package are unemployed?
2. What is the probability that at least 12 package recipients are unemployed?
3. What is the probability that 3 or fewer package recipients are unemployed?(
4. Calculate the expected value, the variance, and the standard deviation for the package recipients who are unemployed?

A coffee machine is regulated so that the amount of drink dispensed is approximately normally distributed with a standard deviation of 15 mm. Find the 95% confidence interval for the mean of all coffee drinks dispensed by this machine if the random sample of 36 drinks had an average content of 225 ml.

Sir Marvin believes that the mean score of students who attend his review class in

Mathematics is 35. Forty five students were randomly selected and gathered their scores. It

is revealed that the sample mean is 38 and the standard deviation is 8.4 points. Using 0.01

level of significance, test the hypothesis.

Classify the following random variables as DISCRETE or CONTINUOUS.

1. Length of a cell phone charger ____________________

2. Number of gadgets in a household ____________________

3. Count of words encoded per minute ____________________

4. Amount of water consumed per day ____________________

5. Sum of burgers sold in a day ____________________

6. Amount of time needed to boil a liquid ____________________

7. Number of channels in a cable TV ____________________

8. Daily count of visitors in a mall ____________________

9. Distance between two barangays ____________________

10.Total area of a rice field ____________________

11.Growth of a child per year ____________________

12.Temperature needed to bake bread ____________________

13.Number of babies born per day ____________________

14.Yearly death due to cancer ____________________

15.Number of mistakes in a test ____________________

Q. Lots of 40 components each are called unacceptable if they contain as many as 3 defectives or more. The procedure for sampling the 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?

Suppose that 3000 drivers in Wakanda were randomly breath-tested on 21 April

2019 and 116 were above the limit of 0.05 blood- alcohol level. On 15 May

2019, 4000 drivers were tested and 98 were above this level.

1.3.1 What additional information would you require before trying to draw conclusion

from these data? (5)

1.3.2 What factors, other than a real change in driver behaviours, could cause such a

drop in the proportion of above-the-limit drivers. (6)

1.4 A set of data has an interquartile range of 20 and a lower quartile of 6. If the data

is symmetrical, calculate the value of the median.

A jeepney can accommodate 16 passengers. If 𝑋 denotes the number of male passengers in the jeepney when it is full, what are the possible values of 𝑋?

A bus can accommodate a maximum of 60 passengers. If 𝑋 denotes the number of male passengers, what are the possible values of 𝑋?